Is he my boyfriend? Help!

I met this guy and he was very nice and sweet and I became very interested in him instantly. Just for some background, I go to graduate school and I am 26 years old. I will be going to medical school after this year. I had a tight schedule in the school year but we found dates to see each other. He is 31 years old and has his own company. He doesn’t have a building/office but does work through calls. He doesn’t have a solid schedule and just makes one along the way depending on the clients.

Let me tell you, he is the most caring, gentle, and courteous man I’ve ever met. He shows the world that chivalry is not dead and makes me feel like a princess every time I’m with him. He always makes sure I get on my proper transportation, walk me to my car or Uber before he goes, and always asked me to text him to make sure I got home safely. He always pays for everything and makes me laugh so much. So actually, there are no complaints about him except that he was timid. I felt that he was giving me mixed signals at first and after a lot of confusion, I finally I told him I liked him. He said he liked me too and this was after about 7 dates.

After some time I wanted to clear it up with him and texted him a “what are we?” text. (I chose to go this route bc it seemed like he opened up more when writing/texting). But then he asked to speak to me on the phone.

He basically told me he doesn’t really know about us yet because actually, he was interviewing jobs (I knew this on date 3) and might leave my city (I didn’t know this). He is even interviewing as far as China (he declined this offer eventually tho). So at that phone call, I “broke” it off with him. We could text and be friends but not see each other until he finds a job. He actually wanted to hang out more but I said no. However, I actually did not text him at all even though I said we could...and he didn’t either. This lasted about 2 months.

I actually thought I was fine with my decision and started dating other people. However on the dates, I JUST COULD NOT GET HIM OFF MY MIND and compared every one to him, and the people who I did date did not match up to him. Eventually, I shot him a text asking how was he, to which he replied like nothing happened. He gave me a light-hearted full paragraph with many emojis...I was tbh surprised.

Fast forward to now which was a month later, we started getting closer and he ACTS LIKE A BOYFRIEND. We text each other everyday, go on dates, eat together, Netflix and chill, do work together, cook together, travel to other cities, he surprises me with gifts, etc! The farthest we’ve gone is say ‘I miss you’ and he calls me ‘baby’ sometimes. He kisses my forehead so lovingly when we’re hugging or in bed and that to me is very boyfriend like. We even hold hands in public. He even agreed to meet my friends! Eventually we started getting intimate and I have no complaints about it so far.

Then a friend who I know was interested in me asked me out. It lead me to talk about us (again through text) and he basically said I can talk to him or I can talk to someone else, he will respect it either way. But he just asks that I tell him. As for him, he’s not talking to others and isn’t interested in doing so.

When he said that, I had to meet him half way even though I really wanted something more. That was the last time we talked about us. It’s just so hard and confusing because he doesn’t know if he will stay or not, it really depends on the job and when and where he gets it. After much speculation and talking to friends about it, they said our little talk basically defined us being loyal to each other without saying the word loyal. With the same philosophy, we were already in a relationship without calling it a relationship— we just don’t know it yet.

So my question is...are we?

How should I approach this situation?