I actually have European ancestors who survived the plague and because of this, I have been told that I am more immune to diseases that broke out back then and that does make sense. So I can imagine that the chances of me contracting the plague wouldn't be as high per se. But now, my concern is what I might be carrying. I am not a medical professional so I'm unsure. What are the sicknesses we carry today that they didn't have, and would I carry these and spread them to people back then, therefore killing them? I think our immune systems are stronger because of vaccinations and they didn't have those in the 14th Century so I would assume they'd be a lot more susceptible to diseases we are actually immune to. Am I correct? Accidentally killing them would be a flippin disaster.
I think you would have to worry about the opposite happening: you getting diseases from them. We have vaccines, true, and Europeans are even immune or at least have heightened resistance to a certain strain of the plague. There were and are multiple different strains of plague.
That said, there is a lot of other stuff than just plague out there. Plague was nasty, but very rare (besides the big outbreaks of course). Stuff like dysentery and smallpox were a lot more common and modern people aren't immune to those. In fact, I would say modern people would have a bad time in the medieval period (in more ways than one).
I suggest that you check my answer to this question:
I say that taking even harmless future germs - like for example, the future germs that live in your guts and are vital for digestion - centuries back in time will change the genetic of medieval germs. Thus it will change the future evolution of new germ species from those medieval germs. Centuries afterward, there were be different species of harmless and harmful, even deadly, germs than there otherwise would have been.
What are the lifeforms that most influence how long humans live? Germs. So by spreading future germs in the past, and past germs in the future, the time traveler will change the way germs evolve into new species, and thus will change the evolution of new disease. So people will die who would have lived, and people will live who would have died. And after a few thousand years, some of those people will become the ancestors of every human alive. So the time traveler will replace all the humans living thousands of years n the future with a total different population of humans in the future.
Thus the humans thousands of years in the future will have a strong motivation to use time travel to prevent the time traveler from erasing them from existence and replacing them with a totally different set of people. And if they can figure out a way to time travel without spreading or picking up any germs from the time traveler's era they will time travel to stop him.
First, I think you should consider the possibility of the time traveler to get vaccines for all the old diseases from back there, when possible. (And a few antibiotics, which will be super duper effective in the past) This get all the "you will die first" out of the way.
About your own diseases, I don't have a strict answer but you could minimize risks by doing a small quarantine and going though a decontamination before traveling. This way, there will be few chances of you contamining anyone or at least with nothing too dangerous. You'll still have you own internal flora but if you don't kiss anyone on the first days, neither shit or puke on anyone, it should be good. At some point, what you eat there will change your own flora (you may feel a bit sick, but like anyone traveling abroad) and you'll be good to go.
The only modern contagious disease I can think of that wasn't around then is HIV. But you'd probably know if you had it, and it's not easily transmitted (unprotected sex, and not all kinds, and sharing blood, stuff like that).
And of course cold or flu viruses, since they mutate often.