Do I have anything to worry about?

My boyfriend & I just recently started living together a few months ago. I am 37 weeks pregnant with our son. We will be together for 2 years at the beginning of November. My boyfriend has been having a hard time finding a job & has been getting text messages from this girl he calls Big Bad Mel. She started off with messages trying to see if shee could get physical with him because apparently they were together a long time ago (before him & I met) in that way & she wants him again. He said he sent her messages to let her know he is now taken, happy & having a baby with his girlfriend (which is myself). He has not been very physical with me lately, intimately that is, since I have been in my last month of pregnancy. He says it's because he feels bad about not having a job yet, he's scared something might happen to me during my cesarean since I am on blood thinners from a blood clot in my leg, & he has been feeling sick off & on lately. I feel like I have to push him just to get physical with me when it was not an issue before. I am not normally one to peek on someone's cell phone but I wondered if he was still getting messages from that girl. She has still been sending him messages. Infact they corresponded yesterday. His messages to her are all deleted but the ones from her are still there. He also deletes out the calls out on his phone on a daily basis. It does not seem like they are doing anything but seems odd that he would still be talking to a girl that he slept with before & not saying anything to me about it now. Should I worry because I am at the moment & it's hard because I am an emotional wreck as it is from this pregnancy.