How soon can a kitten be treated for fleas?

I am new here and I just adopted a kitten a few days ago. Her name is Jasmine and she's about 7 weeks old. She turns out to have fleas, and so far I've been able to pick out most of them with my fingers. The flea comb is not working at all, even if I see a flea and even if it's dry or dipped it hot soapy water I can't get them with the comb. First time I picked out about 7-10 of them, and after that it's been about 2 a day. I believe there can still be a flea or two left, but not many.
I do get nervous about them getting into carpets etc. How or when do you know that you have a flea problem in the house? And when can I give my kitten flea treatment? What kind would you suggest?

Take Jasmine to the vet ...

Yes, only the vet can treat the problem in hte right way. Don't buy flea treatments as they can be really dangerous, no matter what it says on the label.