No sign of me on social media.... is that a red flag?

I started dating a guy a little over a year ago. Our relationship for the most part has been pretty great. He spends the majority of his free time with me, is always responsive and texting me all the time when we are a part and shows me he loves me by surprising with me with flowers or does other nice things like has a bath waiting for me after a rough day. BUT......
I feel like he hides me on social media. In the beginning he posted a pic or two of us and allowed me to tag him in a few things on fb. I am not big on social media so I am not all concerned with being fb official and all that and I am not crazy tagging him every day in dumb shit, just a pic or two every other month or so. In the beginning he had his profile pic of the two of us, then after a fight one day he removed his profile pic of us and added the restriction so he has to approve tags for them to appear on his time line. So now I tag him in pics and they never appear on his fb BUT he accepted pictures of him on a ski trip with friends and a few other pics with friends. I started to find this suspicious. One day he went to the bathroom and handed me his phone. It was unlocked so I went on his fb and into his messages. He had been messaging back and forth with a girl for months. Based on the few messages I read they never actually met. I confronted him about it and he admitted it was stupid but nothing was going on. He said he started chatting with her one night after we had a fight. Ok so I forgave him but he continues to not allow pics of us on his facebook. He introduces me as his gf and I have met his family etc... so that is all good and normal but I feel like I can't trust him. He also adds random girls as friends (he def slowed down but still does it once in awhile). I have told him more than once that annoys the shit out of me and makes me feel like he is still looking or keeping options open. So tonight I see he became friends with some girl. I asked who she was and he said the daughter of an older guy he works with. OK so I asked how do you become friends with the daughter of a coworker? Who friended who and did you ever meet her? His response was I am not getting into this with you. You have nothing to worry about. You are the only one I want and to prove this he deactivated his fb instead of explaining why he hides me and friends other random women. I am seriously considering ending things. I feel like there is a difference in being private on social media and hiding things or trying to appear as though you are single when you are not. I know guys will look and maybe even flirt but there has to be a line drawn. These things he has done certainly has the potential to turn into full blown cheating. Do I think he has cheated. I honestly do not think anything has actually happened but.....how should I feel about all of this?

I feel bad since this post never got any attention.

Well, good for you on talking to him about things. Good communication is the center of healthy relationships. Why wouldn't he have your relationship appear on his Facebook page, and also, feel free to express that that makes you feel hurt that he doesn't ever allow the pictures of the two of you together to appear on his feed. You can say that it makes it feel like you're not special. You should be facebook official in my opinion, you're his girl, he should want to show you off!

The random girl thing is weird, its one thing if they're adding him, and he ran into them at social gatherings or they're someone's girlfriend or from work, whatever and they added him. But for him to seek random girls to add is odd. I can understand how that would bother you.

I dont think he cheated, but it's a moment that makes you question things, like, is he looking for a replacement or what? Is he trying to prove something to himself, that other women might desire him? Or what. I don't know.

I agree. I think you're right for feeling the way that you do.