It doesn’t sound to me like everything is “good” Constant fighting is a symptom of a much bigger problem that shouldn’t be ignored. You both have reasons not to fully trust the other. I do wonder if your conflict over what you call “insignificant stuff” is a way you two are dancing around basic issues of trust.
You are right to be concerned. Your relationship will not survive if the two of you don’t figure out how to manage conflict, how to communicate about difficult issues without getting defensive, and generally how to comfort and reassure each other when the going gets rough. You both have past hurts that are getting in your way.
If you want this relationship to last, I urge you to seek out a couples counselor. If you could figure out how to stop the fights and work as a team to solve problems, you would have done it already. A counselor can help you each heal from the past and can coach the two of you about how to manage conflict and anger productively.
I wish you well.