Fleas won't go away

Since finding fleas on my cat, I give him daily brushes and showers with flea shampoo. My boyfriend sprays the room with flea treatment, on the carpets, sides, cat tower, bed, literally everything. I've spent a lot on relatively expensive products and nothing is working. I brush him again the next day to find more. What do I do?

He is a ragdoll, and if nothing works within the next few weeks we are even considering fully shaving him. He is also a fully indoor cat. We don't take him outside. I don't understand how he's even gotten fleas in the first place.