Sorry, 2nd time asking since no answers, but i need some girl help..?

hi, me and my gf have a longdistance thing and shes younger than me. in the past few months, things have gotten a little shaky though. she tells me i dont open up to her as much as i use to and i think it has to do with when she cheated cuz i upset her one week. she thinks i dont care about her, when in all reality, i couldnt care more about another human being. we've been making alot of future plans like marriage and etc, but i cant help but still get myself into these very random fights. For Example, today, we were all happy and talking, and i know her and my brother are bickering and making pics and editing them left and right to compete with each other. well i jokingly said my brothers art owns hers. and she took it as a direct crack at her and we had a little insult flinging back and forth, broke up for about 10 minutes, and then talked a long time until she went to bed and i signed off and did my own thing. i'm curious what i could do to reopen to her. any advice for me?