Different outlook? What do you think?

My boyfriend and I have been together for three years and are very serious. We have been TTC for a few months now (no luck yet) and are beginning to plan our wedding. A few weeks ago his phone was on the charger while he played basketball so I decided to take a peek. I've never looked through his phone before but I've always been curious. He was texting this girl he works with saying things such as "hope you're having a great day!" "Miss you at work" "see you Thursday in class" (they are both teachers). Then his brother texted him asking if he had messed around with her and he said no. Now of course I confronted him and he said he's so sorry he's a jerk all this and I forgave him. 
Few weeks later I went to connect my phone in his car to his Bluetooth and saw "her name's iPhone" as a choice!!!!!! He says she must have done it as a joke or the car picked up her phone when she went to grab something from it one day (which I didn't buy for a second). We have been kind of rocky ever since. I've asked him a million times he always denies it. 
Yesterday I had shared a photo on Facebook saying "my man is my best friend" and I tagged him in it. This girl liked it! Then today she sent me a friend request on Facebook. He told me to block her and pay her no mind. But I'm not sure I can. 
Now this may sound dumb, but to me, it's serious. It's serious because it could be the start to something bad and I refuse to be played with. So if I can catch this stupid stuff before it happens, I will. Please no negative comments I'm looking for advice and opinions. Thank you ❤️