Do we need to define the relationship?

The guy I've been seeing for a few months has really started to act like my boyfriend lately. Sleepovers, taking me on dates, making future plans with me, pda in front of his friends. The only thing is that he told me a few weeks ago that he was talking to someone else. I don't see him texting her anymore and it definitely feels like we're in a relationship the way we treat each other. I just don't want to press the issue, but I'm also a lady and going a little crazy inside 😝 how do I bring this up with him, or do i?!