I have treated some pretty severe flea infestations, and it can be rather challenging. The key is a total, holistic approach. The area must be vacuumed a lot, and that means all furniture, under furniture, drapes, etc. Fleas/eggs can live an amazingly long time without food (you/pet), and can live on hard surfaces, in joints between floor planks, that would seem inhospitable. After a very thorough vacuuming of everything, it's time to spray the area, furniture, rugs, etc with insecticide, and a growth regulators. Raid makes a pretty good canned product, but I like to use a 1% strength Permethrin, mixed up with an added growth inhibitor.
After spraying, you might see what seems an increase in flea activity, but this will die down. Vac again every day, and perhaps spray again in 5 days or so. Persistence is key, and if you miss one spot, you could have issues... That means closets, under couches and chairs, drapes... I also add a cat/dog flea collar to the dust collection system of the vacuum, to keep live swept up fleas from getting out. Doesn't hurt to spray this dust container either. I will also spray the yard, patios/deck with this same spray, and it really, really works.
Never had a situation that I did not win, it save s a ton of $$$ over a pro, and you may get better results than a pro. Good luck, I know how frustrating this can be.
Edit: Forgot to mention, make sure to read the application label very carefully. Permethrin is a very safe insecticide when used as labeled for people and dogs, but cats are very sensitive to it. Accommodations would need to be made. Permethrin in fact, is what certain tick repellent clothing is sprayed with; I do it myself as a defense against Lyme disease carrying ticks, and it is extremely effective.