Tiled basement floor painted with semi-gloss paint. Should I wax it?

Hello, we have an old vinyl tiled basement floor, we cleaned it thoroughly and painted it with regular semi-gloss wall paint. After a few coats, I am wondering if I should put floor wax over it. I know there is floor paint you can buy, but we wanted to use up some paint we already had to save money. I tested in a small area putting some floor wax on and I don't know if I rubbed to hard, but the paint came up in a few spots. I just want to protect it so it won't peel up if wet, or if shoes scuff it, etc. Any ideas, I would appreciate it. Thanks!