Buddy bit me recently right on the nerve between my thumb and index finger. It made my hand numb and achy for about a day. Then it healed and now I'm fine. The sneezing could mean he's just alergic. Or could be a conicidence.
There are a few disesases that rats can have but they're all really rare so it's pretty unlikely she infected him. But if he starts showing any more symptoms obviously get him to a hospital and make suee they know he was bitten by a rat.
If he gets a fever, or if you start to notice a red line going up his arm from around the area of the bite, go to a doctor quickly. Not sure if the sneezing is related, but the slight numbness could just be irritation from the bite or it could have been near or on a small nerve like Dan203 said. Is it swelling a lot? A little swelling will be normal, but if it really puffs up, doctor.
It's probably nothing, but it's a good idea to watch it for a couple days. Did you wash it out very carefully with a lot of hot water and antibacterial soap?Scratch in there with a brush or fingernail with antibacterial soap to really get everything. If you're very nervous, try packing in sugar too or raw honey to help draw out other stuff the soap and water may not have got.
I'm kind of old school... I still put iodine on any skin break... So far, at least, I found it gets pretty well into the wound and kills most things that can infect you. And yes, it burns like you know what, but that's how you know it's getting in there and working.
I even put iodine on a mouse pup with tail rat... and it stopped the infection on the spot... the black part of the tail fell off, but the mouse lived a long and healthy life.
It's about the cheapest stuff in my medicine cabinet, it seems to last for decades and it's come in handy more times than I can recall.