I don't think he's cheating, but he is acting shady

So for starters I'm 27, my bf is 33, and we are about 3 weeks away from having our first baby. This weekend his phone was in my swim bag after a day at the river. I started taking everything out of the bag and I noticed his phone lit up. There were 3 unwatched Snapchats from a female named Desiree (and I've been with him long enough to know he doesn't have any female friends by that name, so there's something wrong with this). So I watched them (i didn't snoop through anything else in his phone, just watched those to see who the hell was sending him snaps). I watch them and they are just 3 selfies of her trying to look good with her boobs about to fall out of her shirt. I also notice that I recognize this girl. (I work for CPS and recently had an investigation on her and her kid. She's a very nasty trashy girl and so is her boyfriend.) So I confronted my bf about it. I straight up told him what I saw and asked him why he's snapchatting other girls. He told me he doesn't really know her, he just met her through a mutual friend type connection on Snapchat. He said everything between them has been innocent, nothing inappropriate, she just sends pictures sometimes and asks how his day is going. I told him I knew her from work and #1 she's completely trashy so if he's cheating he better raise his standards, and #2 I'm not comfortable with him snapchatting other chicks he just randomly meets online, even if he says it's innocent. He told me he was sorry and didn't mean anything by it. He said he would delete her and said he doesn't like Snapchat because it's too easy to get himself in trouble. He promised he wasn't cheating and said he has no intention of cheating or leaving me. He said he's happy with me and can't wait for the baby so we can be a family. I believe him. I really do. But I think there's more to it.... why even entertain some random chick online if you're truly happy? What do you think?