Hello Kate,
You’d notice the flea bites if you were getting bit. The reaction is similar to a mosquito bite. In rare circumstances people don’t display a reaction, but in all likelihood the fleas aren’t biting you.
It’s somewhat strange that you’re seeing fleas in your room if the cat doesn’t go in there. I would assume you’re bringing them into the room yourself. They may be hitchhiking on you. Of course, I can’t be certain without knowing the full details of you situation and environment.
Immature fleas develop within carpets. Once they reach adulthood, they move to the top of the carpeting to wait for a nearby. If you’re the nearest warm-bodied animal, they’ll jump on you. When they jump on people, they almost always land on socks.
Cat fleas don’t live on people, as humans make poor hosts. They may bite people, but they’ll leave soon after. In your case, it appears they’re leaving before they bite. Perhaps they can’t find access to exposed skin.
In your situation, it may be a good idea to purchase a flea trap and place it in your room. Flea traps are poor solutions for ending an infestation, but they’re very helpful for assessing flea populations. If the trap collects relatively few fleas, I’d assume the fleas are hitchhiking on you. If the trap collects a large number of fleas, it probably means fleas are developing in your room’s carpet, which means your cat is somehow getting in there without you noticing.
Similar to the trap technique, there’s something called the “white sock technique”. Just walk around your room with knee-high white socks for a few minutes. Then count the fleas on the socks.
Hope this helps!
Adam