Found out the I “cheated” and I didn’t

A week ago my GF went through my phone and found a text that I sent to another girl asking to check “his nads” she was super pissed and thought I was cheating I tried telling her it was just a dick joke and that the girl had a boyfriend and I didn’t even like her like that but she wouldn’t listen we’ve been having a hard time and were thinking of breaking up so when this happened it just got worse, I was gonna break up with her anyway but now I feel like I was accused of cheating and I didn’t so I’m gonna break up with her I just want to know if I’m an ah for still feeling like I was wronged?