Is he cheating?

A couple of months ago, I was helping our son use my husband’s phone to watch YouTube and he must have opened his Instagram messages because he handed the phone to me asking for help and it was in his messages screen. I went to switch it back to YouTube but a message caught my eye to another woman. I clicked it and saw he had messaged her about “great breakup songs” while I was in labor with our baby. I switched the phone back to YouTube and gave it to our son and didn’t say anything about it. Yesterday, my husband and I started arguing about him not helping out much with the kids and seeming “checked out” and I brought up the messages and asked why he would be messaging her while I was in labor. He said he had no idea what I was talking about so I asked him to grab his phone and I could show him and give him the chance to explain it. He handed me his phone and the messages were gone but it said “3 days ago” next to her name for their last interaction. I instantly felt sick and asked why he deleted the messages and what was 3 days ago. He said he had no idea. I asked him again and he started getting noticeably flustered. I asked if I should message her and ask her and he immediately said “you know what, maybe we’re not right for each other since you don’t trust me”. All of these things are such red flags to me and I asked him what was going on and he “swore on our children’s lives” that nothing is. He has since apologized about it, without really admitting anything, and has been posting about how much he loves me on Facebook almost daily, which he has not done in months. Today he said he did remember messaging her about a song because she “posted on her stories that she needed good breakup songs” and then 3 days ago “liked a quote about life” on her story “but then felt guilty and like he was betraying me so he deleted everything”. I really don’t know what to do or think. Do you think he is cheating?