My lower back has been killing me for couple days and i had sex last night and my left lip little swollen but it's on outter lip and it's a purpli?

Unrelated: Your low back pain and swollen labia are probably unrelated. The labia swell with very little trauma or as a reaction to a lot of chemicals ( allergic type reaction) and the sex last night could have bruised the labia. The low back ache is probably due to something else entirely like muscle strain, a bladder infection, or even a pelvic infection especially since it started a few days earlier.