I'm not a big fan of "zombie viruses". 28 Days Later may be the best of these, it's a rabanoid virus by the looks, the zombies eventually die of starvation, and the method of transmission means it might be possible to affect the victims as quickly as depicted. But generally it's a bad plot device.
You've got a few problems with the mechanism of hostility/aggression. But nothing that can't be fixed with a little hand-wavium. Instead of it infecting the sites of the bites, this will metastasize. Tasmanian Devil disease is a transmissible cancer... the cancer cells originated on an individual many decades ago, but his cell line lives on in others. Just before it kills them.
The Tasmanian devils aren't biting because of the disease, they're just nasty little shits always fighting each other. Maladaptive behaviors, eh?
We do need your variant to affect the brain. And massively. You want extremely intense aggression, you want physical debilitation, lack of reason (or even personality). That affects all parts of the brain, so a purely mechanical etiology is out. This cancer will preferentially attack the human brain. All lobes, or almost all of them. But we can also throw in some skin lesions and general necrosis to give you the zombie look.
The cancer's aggressive growth means that even if oncological treatments worked, they're biting their doctors long before they can get a course of chemo. And the brain damage is so extensive that the condition will be irreversible too, if that matters to you.
This won't be a "3 hours later, full zombie" thing. The tumors themselves that cause this will be small (but many of them, thousands) which is enough to cause the change sin behavior and the icky looking sores and blooshot eyes and so forth. Probably looking at least 24 hours before infection spurs full conversion, but if the story allows and you want it to be more realistic, longer would be better. 72 hours, or even a full week would be enough for pea-sized tumors to occur.
Realistically, these things will burn out really quickly too. They get a few days of shambling around at most. Some percentage of them would go really quickly, when the tumors infiltrate vital organs other than the brain. If it gets the heart or the lungs or kidneys, they'd probably drop before the other zombies. A few others will just stroke out when the tumors in the brain pinch off blood flow. Conversion rate won't go above 60% or 70%, the rest will just be made dead quick, possibly even before they could attack others. A smaller number might display truly bizarre (not necessarily zombie) behavior, as the infection randomly ruins parts of their brains. OCD behaviors, walking in circles, whatever.
Classic zombie mob scenes might not work. There's no plausible mechanism for them to refrain from attacking each other. Not sure that's necessary though.