I'd go with the flea theory. Them little buggers will tear you to bits. Do they itch A LOT?
Fleas only live on a host (pet,you) about 10% of the time. The rest of the time they live in your house, in your carpets, any place the pet sleeps or goes. They are hard to kill and need a specific regiment of extermination to kill them. Fleas lay eggs all over and the eggs take 2 weeks to become full grown fleas.
You have to get spray from an exterminator. The stuff you can buy at the store is worthless. You then vacumn really well and empty the bag. THEN you get either a garden sprayer or something that will spray your entire house with a fine mist. Spray the entire house. The spray is residual which means it will stay on the carpet for a bit.
THat is step one.

Step two is to spray again in exactly 2 weeks as then you kill the eggs that are now full grown adults. If you skip this step, the eggs will just make more fleas and you will never get rid of them. A better option is an exterminator.
Nothing you can put on or bathe the cat in will get rid of fleas as they are only on the cat a very short amount of time. IF you see fleas on the cat you can rest assured there are thousands in your house....
Fleas in your home almost always bite on the legs. If nearly all your bites are below the knee it's likely fleas. They jump from the floor as you walk by, bite you and jump off. They're pretty small and hard to see but you can see them if you pay attention.
There is a fairly easy way to see if you have a flea infestation. Put on a pair of white knee socks. Walk all round the house a couple times bending over every little while and looking carefully at your sock. Do you see any fleas? They show up pretty good on white socks.
Good luck. I hope it is fleas as even though they're hard to get rid of, at least you can get rid of them and get rid of your problem at the same time.