If your house is that infested with fleas, might I suggest sending your cat to be flea bathed, removing your chin from the home, and bombing? If it is to the point where fleas are jumping around, I don't care what medicine you put on your animals, it isn't going to get rid of them. Fleas are my worst nightmare because of all my animals.
I won't even use topical flea medicine on my dogs or cat because there have been so many instances of toxicity. I bathe them in dawn dishwashing liquid, bury my carpets and furniture in diatomaceous earth, and treat the living heck out of my yard with beneficial nematodes. I have not had a flea here in four years (knocks on wood). You can even rub the diatomaceous earth all over your cat and it does a fantastic, nontoxic job. You could have your chin dust with it in his dust bath as well, since it is food grade and edible. Sprinkle by your doors, around the foundation of your house, etc., as well. I leave it on the carpet for a couple days and walk all over it so it works its way down deep (put it on the furniture too), then vacuum it up. No more fleas. You have to treat your yard though. You will never get rid of them if you don't get them at their source.