Is my ex doing too much??

We broke up officially about two months ago. It’s actually been longer because we’ve been on a “break” since September. We’re married so we have the same phone plan. Nothings changed yet but after we made the breakup official, he all of a sudden starts looking at my call logs with his mom, who’s also on the phone plan. I’ve been texting a guy as a friend and we talk on the phone a couple times a day so he saw that and started asking me about it and ended the conversation with “fuck off”. I don’t see the big deal since we’re broken up and I’m kinda pissed that he was looking for some shit and went to his mom with it. I know him and his whole family are probably talking shit about me. After we broke up we agreed to keep it cordial and I said I won’t ask him about other people he starts seeing or what he’s doing and he’ll do the same with me. Clearly that’s not happening 🤦🏽‍♀️ what should I do from here?