A remark at the beginning: In a world where real-life vampires existed, there would certainly also grow a lot of myths about them. So we would have to distinguish between in-world real traits and in-world myths (that is, things that are commonly ascribed to vampires in that world, but are not true, or not entirely true). Therefore the real task would be to devise a pathogen and corresponding vampire traits that cause the commonly assumed traits to be plausible to the general population, given the actual traits of the infected.
Note that if the pathogen appears in a society where vampire stories are already culturally ingrained, it is quite likely that the fictional vampire traits would be projected to the real-world vampires, as long as some traits are a good fit.
So, let's look at what traits real-world (as in, real in that fictional world) infected people might have that would make them to be seen as having the traits of vampires.
Drinking blood for nutrition
The main theme of vampirism is, of course, that vampires drink the blood of their victims, and those bitten then become vampires themselves. So how much of that could be true?
As other answers already explained, nutrition just from blood is unlikely, as you'd too much of it to live from. However, what is definitely possible is that a pathogen gets transferred on a bite; that's for example how rabies is transferred. Now while rabies certainly makes animals bite, it doesn't make humans bite. However I found this article which details that aggression after infections is not quite uncommon, and even cites a case where a girl bit her father several times, although admittedly from the description, the biting doesn't look like a specific result of the illness but just part of the common infection.
So while there is no direct indication that an illness could specifically cause biting in humans, I'd say there's nothing that specifically indicates that it could not be possible in principle. And indeed, for an illness that is transferred by biting and that is human-specific (that is, it cannot simply spread through aggressive animals, like rabies can), it would make sense to cause this behaviour, as that would spread the disease.
Indeed, for effective spreading, it would be advantageous if the pathogen got directly into the blood of the bitten, so it would also make sense if the infected developed a specific appetite for blood. However according to Wikipedia there's little evidence for specific appetite in humans, and the few examples cited are for specific elements. So it is unlikely to be caused by a pathogen.
So how could the perception of blood drinking be caused?
The infection spreads through bites. The victim is more likely to be infected if the bite reaches the blood stream. Thus it is commonly assumed that the infected specifically long for getting to the blood stream.
The infected get pale (more on that below). This seems compatible with the idea that their blood is sucked out.
The infected live separate from the uninfected humans, both for their light sensitivity, see below, and the fact that they are feared by the general population (and in turn have to fear the normal population, as those are likely to kill them). Therefore non-infected people generally won't see infected people eating, reinforcing the myth that they are living off the blood they suck from the victims.
There still remains one problem: Why would vampires seek out uninfected humans? Well, from the point of view of the disease it would make sense, but I cannot imagine a mechanism that could provide that.
However note that the actual rate of people being bitten need not be that high for the perceived rate to be high. It's just like crime in our real world: The actual violent crime is generally going down, but the perception is that the world is a very dangerous place. So maybe in that world, actual bites are also a relatively rare event (and most of the infections happen through different infection paths), but get blown out of proportion in public perception.
One of the symptoms of the illness may be Pallor. Note that the list of causes includes tuberculosis, so it definitely can be a symptom of an illness. In addition, they will likely have little pigmentation, either just from never being in the sun, of from an additional Hypopigmentation which can also be caused by illness (the linked Wikipedia page lists leprosy as possible cause).
Avoiding the sunlight
Of course, the idea that a vampire decays into ashes when exposed to sunlight can only be a myth. However what is realistic is that the vampires would have to avoid sunlight, which would then inspire/reinforce that myth.
This could have several causes. One is Photophobia where one of the causes listed in the Wikipedia article is excessive response in the central nervous system; this fits well with the aggressivity theme above.
Besides that there is also Phototoxicity: The pathogen could produce a substance (or make the body produce a substance) that is phototoxic. This would also mean that exposure of vampires to skin would cause visible effects (although not immediately), something that could well add to the myth about sunlight killing vampires.
No mirror image
This is of course physically impossible. However, it might be that the infected people simply avoid mirrors in order to not have to see their own deceased look. This may fuel the myth that they are not seen in the mirror.
Sleeping in coffins in burial crypts
They most probably won't sleep in coffins. But since they have to hide from the sunlight (see above), they have to seek dark places to hide during the day. Moreover they might want to do it in places where non-infected people are unlikely to come. A burial crypt might just be the ideal place for that.
Garlic helping against vampires
Well, garlic allergy exists. From the Wikipedia page:
Garlic allergy has been known since at least 1950. It is not limited to hand contact, but can also be induced, with different symptoms, by inhaling garlic dust or ingesting raw garlic, though the latter cases are relatively rare.
So if the vampires all develop a garlic allergy, garlic will indeed be a good means to keep them away. And contact with garlic will indeed have very bad symptoms for allergic people:
The affected fingertips show an asymmetrical pattern of fissure as well as thickening and shedding of the outer skin layers, which may progress to second- or third-degree burn of injured skin.
This may well be interpreted as a sort of decay by someone seeing it.
However, I've not found anything indicating that infections can cause allergies to unrelated substances.
Could an illness sharpen their senses? Well, there are indeed some possibilities.
One thing they'd probably have is a better night vision. In the Wikipedia article on Accelerating dark adaptation in humans I found the following:
Rod cells are much slower to adapt to the dark and it is believed to take days for these cells to reach full dark adaptation.
Since rod cells are precisely those used for night reception, it implies that if you are continuously in relative darkness, your night reception should be better than that of people having daily sunlight exposure.
Also there might be effects similar to the blind being better at hearing which according to the linked article is confirmed. Since the vampires won't exercise their day vision (like the colour perception systems) much, their brain may reassign its resources to night vision, or even to unrelated senses like hearing or smell.
Speaking about smell, there's also Hyperosmia which causes a decreased threshold of smell; that is, you smell things you wouldn't smell otherwise. The Wikipedia article indicates that there are some substances that might cause it, so it's not unconceivable that the pathogen might produce one of those substances.