Does this sound like narcissistic behavior?

My boyfriend and I have been having some major issues in our relationships. One being that he has a bad habit of messaging girls emojis such as “❤️😍” and things along those lines. He also doesn’t know how to talk to me. His communication is literally shot. I’ll try to be as calm as possible and he cuts me off telling me to “shut up” and that I’m insecure or a cry baby. I tell him all the time you never tell a woman she’s a cry baby for expressing how she feels or feeling some type of way at all actually. He continues to say it regardless of me telling him I don’t like when he says it. The time I have caught him messaging a female he did not once apologize. He said he did it because he we weren’t together...... We broke up for literally not even 24 hours! He hasn’t apologized for that yet. Not even looking forward to an apology anymore. Also one day I was over his house and he has a video game. He played the video game for more than 5 hours as I sat there bored out my mind. When I confronted him about it he made up all types of excuses as to why I should be ok with him playing the game excessively while I’m sitting there..... didn’t apologize or offer to try and change his behavior so we could work. He just overall doesn’t try to compromise with anything. I always find myself trying to be “comfortable” with things just so we can be together. When deep down I’m not comfortable and he has over stepped many boundaries that I would’ve never thought I would let anyone cross. 😥