We’ve acted like a couple for a month, but I’m still not his girlfriend?

I want to start of by saying that I know I probably sound very psycho throughout this lol. I met this guy about a month ago. He’s in the marines and he was on leave. He gets out in 6 months and he’ll be moving back to our home town.
Ever since we met, we both just instantly liked each other a lot. When he left, he said he wants to “make this work” and we can set a goal to see each other at least once a month for the rest of his time in the military. We FaceTime every single night. I just flew up to his base to spend a week with him. We went hiking, went out to eat, did a lot of fun stuff.
Then... one night I was drinking (a lot) and I acted crazy. He was showing me pictures on his phone of his trip to Germany a couple years ago, and there was a pic with his arm around another girl. So I got upset, and it went downhill. Eventually we were arguing and he made a comment that he’s not my boyfriend, and he wants to take it day by day because trust takes time to build. I didn’t argue with him I just said okay... and then I started crying 🙃 again, I was really drunk, I didn’t even remember this. I got emotional and I was like “I flew out here to see you!” And it was a whole mess. The next day we talked about it and he said he wants to take it day by day, he doesn’t want to stress and he doesn’t want to deal with jealousy or manipulation. I understand that and I told him last night was the alcohol, and I apologized.
Everything has been good since, but now I kind of don’t know where I stand with him. We’re not dating but we’re practically a couple?
We’ve acted like a couple for a month, but I’m still not his girlfriend?
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