Best way to get rid of fleas from your house?

Hi All!
I have a cat who has/had fleas.
I’ve de-flead the cat but I keep getting bitten!
I’ve got about 30 flea bites on me and worse is that I’m allergic, so they are 10x as itchy and then go bright red, blister and take about 2 weeks to go away. I’ve just found some new bites on me tonight as well.
Anyone know how to get rid of them?
I’ve vacuumed, I’ve got fly spray that is for fleas – I’d rather not bomb.
Can fleas live on a person?
I feel like I must have some living on me.
ps: I’ve tried the bowl of water and soap but no fleas jumped in.
Thanks!