Is it normal for couples to argue to the point of tears? What should I do?

From my personal experience I would say yes , It is normal . It depends what you guys are fighting about. Sometimes you start arguing for something little and you end up fighting. I used to fight a lot with my boyfriend just because I didn't trust him , but we fixed everything and now I do trust him. It would work just give it time . Go out together and have fun so your minds can forget about all the stress.