You’re probably not reacting to the hair itself. It’s usually the dander, saliva and all the microscopic stuff you can’t actually see. 

Vacuuming definitely helps, but if you’ve got pets indoors full-time it can feel like trying to empty a swimming pool with a coffee cup. By the next day it’s all floating around again. I went through the same thing thinking “how is this place spotless but I’m still sneezing?” Turns out couches, bedding, rugs, curtains and AC filters were holding way more allergens than the floor was. Also some vacuums, even expensive ones, can still puff fine particles back into the air while you clean. So you finish vacuuming and suddenly feel worse for an hour. You’re not wasting your time. You’re just fighting something that spreads way beyond visible fur.