First relationship fight, what to do after?

My boyfriend and I have been dating for 4 months since a few days ago and we recently had our first relationship fight. It was concerning how every time we made plans together, it would never happen due to something always happening the day of or day before concerning him. The last time we saw each other has been a week ago, where we were supposed to have plans but he had to go home because he pulled an all nighter in addition to being sick. That made me angry and so I brought it up over text the next day wanting to talk about it. He ignored me that day, and then waited until the day after to reply back. Yes, yes, texting isn't the best way to solving problems, but I couldn't meet up with him as you know the fight is also about not being able to meet up with him when planned. After our fight, we resolved much of what we argued about. We told each other how we felt, and in the end how we would improve and such. I thought it wasn't too bad of a conc lusion. The day after, he was a bit cold, for example, instead of saying the usual "Morning Babe <3" it turned to a "Morning!" I know I shouldn't expect things to smooth out so quickly and understood there was still some tension and awkwardness between us, so I let it go for a day. The next day turned out to be the same, and here I am today, 3 days later, and him still acting the same way. A bit cold, and a feeling of distance. I feel like I'm the one trying hard to keep being sweet and loving to him and keeping the convo going as well as I can, while he just answers and that's all. He hasn't even asked me how my day was the past days, or what I've done. Considering not having been able to see him for a week, should I ask him to hang out? I feel that hanging out again finally would help us move on and get back on the right road, a better one than now, but then again I feel that I should instead wait for him to ask me to hangout instead because I've asked him out many times, where he hasn't actually been able to show up. I actually do want to see him as I miss not spending time with him. I wonder if he feels the same. Should I wait for him to ask me? Will this tension go away soon, as he might need more time to cool down? Or am I just being a total worry wart and just relax. How should I handle this coldness; approach him about it, or stop and ignore it?

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