Aw I'm sorry. Fleas are no fun.
Frontline and other topical flea treatments you buy at a vet are pesticides as well, just thought I would mention. Flea collars contain pesticides as well, or else how would they kill fleas? Really almost every product you get for the purpose of killing insects can be classified as a pesticide by the definition of the word. It doesn't necessarily have to be a nasty chemical like everyone thinks of when they think of the word.
Really I understand that you said you are not in a good financial situation but honestly the best flea treatments are the kinds you can get from the vet. Frontline doesn't work well in my area anymore (fleas in some areas are becoming immune to it) but there are other options out there.
Basically you could spend the money on other products, but they don't usually work half as well as the kind you get from the vet and some of them are even more dangerous. You'd probably end up spending more money in the long run because you'd first buy cheaper products that didn't work, then you'd still have to go back and buy the more expensive things that do work if you want to get rid of the fleas.
Make sure to keep the environment clean - wash anything you can like blankets and stuff like that and vacuum a lot. Some people do report success at removing fleas with Dawn if you bath the animal in it but that of course won't do anything for the fleas and flea eggs in the room, just the ones that are actually on the cat at the time. Food grade Diatomaceous Earth (make sure it's food grade) kills fleas, is pretty cheap, and is not harmful to humans or animals other than insects even if ingested. It's a powder, so you could use it to dust your rugs and stuff like that then vacuum it up again.
But honestly yeah fleas can be tough to completely get rid of depending on how bad the infestation is now and I usually just recommend getting one of the vet recommended products like Advantage.