Well, it was a little hard to follow everything.
But it's good to try and stop doing sexual things. Doing everything but sex is still wrong. Including texts. So if you are trying to stop All of that, then that's a good thing.
Are you arguing over sexual things or your past? If not then trying to convince her to "forget" the things the two of you have done will do nothing.
If the arguments are over other things then that suggests other problems. Arguing some I'd ok, but if it's often or over small things a lot that's a problem. You've been dating a year. Most relationships go six months to a year. Of things are falling apart in that time its usually a sign that there is not enough to hold the relationship together. Holding on to failing relationships helps no one. It's usually a selfish behavior (trust me, I know).
But trying to forget about the sexual stuff won't fix anything. In fact it may be counterproductive. You'd be better remembering and learning from your mistakes. As well as being a man and facing them. Trying to forget is to try to deny, which is not a quality of strength. The ability to deal with and learn from things is better than putting your head in the sand about them.
While I won't say it should end, I will say you may want to start preparing for the possibility. If your gf starts a lot of arguments then discuss with her what's bothering her, don't presume to know.