bleeding after sex

So lastnight me and my bf were having sex right before we got in the shower & after we were done we noticed blood on his penis, I didn’t think nothing of it because i heard it was normal for bleeding after sex.. but after i got out the shower , i wiped and saw blood, i was feeling just a little crampy & my lower back hurt just a little bit. (i’m feeling fine now, still just some back pain) ,is this normal? This is my first pregnancy, i just want to make sure before i make a false hospital run. (i’m 38 weeks & 5 days ) i went to the bathroom throughout the night like always and every time i wiped it was bloody. This my 1st pregnancy & I get INDUCED Monday 9/24, is bleeding like that normal for the last weeks ?