<human>: Give me the gist of the text in a nutshell

So I've been with Anne for 6 months and she's the first girl I've ever loved. We started dating this past year at the college we both go to. We have argued a lot over the past 6 months since we started dating. It's gotten to a point where we are both exhausted from the fighting, and even though we both love each other dearly, we are starting to question if we are really good for each other. 

2 days ago, I asked Anne if she would break up with me if I shaved my head and looked ugly, and she didn't really answer the question. This was a shock to me because I thought our relationship was so much stronger than that. I got mad, then she got mad, and we stopped communicating. Later, she texted me that she was sorry and I could shave my head. I replied that I was glad I had her permission (sarcastically, but over text). Then she said she was mad at me, and after I said "for what?", she didn't reply. We fight a lot over small stupid things like this, and its really starting to wear down on me.
<bot>: GF and I fight a lot. Most recent fight is small, but they are adding up. What do i do?