Red flag? Help?

Hi! I just started dating again after a mutual breakup. I (21 yr old female) have been hanging out with (23 yr old male). We’ve gone on several dates and have started introducing each other to family. We’ve both decided that we’re not ready to put a label on things yet but it’s headed in that direction soon. This guy has been truly checking off all the boxes and we have so much in common and agree on everything. He’s extremely thoughtful and always goes out of his way to do nice things and remember things about me. I have however been weary, since my last boyfriend had a lot of problems that he hid from me for a long time. So I guess you could say I’ve been searching for a red flag. I have realized this guy ALWAYS wants to talk about himself. He rarely asks me questions, I just answer my own questions I ask him anyway because that’s the kind of person I am. He doesn’t know how to start conversations or talk deeply about things. He has good responses when he’s talked to but usually it’s just always about himself. When he met my grandma for the first time last night over dinner, I realized he literally would not shut up about himself or more so, stories about his life. It’s great to be relatable but jeez. I mentioned afterwards that he needs to stop talking about himself so much and he apologized. He seems so honest and genuine so I hate to say it but, narcissistic tendencies?? Maybe??? Am I overthinking? Help!!!!