so you've been talking for 2 months now and you've already fought on multiple occasions... I'm probably not the first to tell you that this isn't a good sign but if you guys have moved past that kind of irritation then I'd say that you guys are at least willing to talk things through.
to keep this short I would give a simple apology and say that you're not going to continuously beg him and pour your heart out if he's going to ignore you now I would put this into your own words obviously and try to remove any emotion from it.
example
(I'm sorry for what I said in that text but if you're done with this relationship then I'm not going to waste our time)
I've been in the position of the man that you're talking about. me and this girl were talking for about three or four months and it started off simple and became a complicated situation.
I stonewalled her two or three times because I tried to have a reasonable conversation about a reoccurring issue in the relationship and she decided to blow up on me, now just to put things into context neither of us are the kind of person to get loud but when I brought up this issue that's exactly what she did so obviously that was out of the norm and I wanted her to calm down.
after about a week she messaged me and was was two-faced,, she apologized but said she wasn't sorry if that makes sense. she said I'm sorry for blowing up on you but I'm not sorry for what I said.
after she said that I decided that this issue was not going to be something that we could work through and my time and energy would be spent better somewhere else so we broke up, went our separate ways and haven't talked in 2 years.
some people are willing to work through things and some aren't, if you feel like you are the only one trying to work through things it's most likely a waste of time
I know this comment is mostly negative and I'm not trying to convince you to break up with this person, this is just advice coming from someone that doesn't have all the details of your situation.
tldr make a small apology and leave it at that.