Constant Arguing & Fighting... Help!!!

My boyfriend and I are constantly arguing and fighting over stupid things. We are 100% open and honest with everything in our relationship so when something is bothering us, we bring it to the others attention. We are both jealous people but we know how we feel about each other and we trust each other entirely. The jealousy just honestly gets in the way and we end up fighting about something that shouldn't be an issue. He says that I "beat a dead horse" and I need to learn to let things go and just stop before he gets mad (but this can happen after even 1-2 minutes). We moved fairly quickly and are already living together. I know we are still learning each other and that is a growing pain that we need to get past. Any advice on how to stop the fighting?

The only thing I could suggest is be patient with one another.