ADVICE!!!!!! PLEASE RESPOND I NEED HELP

So my boyfriend went thru my phone and found messages of me and this dude but I have no feelings for him we were talking when I felt my bf was abandoning me and I thought that he was talking to someone but he wasn’t I’ve never had sex with this person just conversation and my bf won’t forgive me he doesn’t wanna be with me because he feels like I stepped out I love my bf so much but y’all know how that goes “if you loved me you wouldn’t do it”. I was explaining to him that it was a bad decision and I’m owning everything and I know I’m wrong but I wanna be with him he says he needs his time and space but I’m afraid that he’ll forget about me like I’ve been trying everyday to show him that I love him and that I’m sorry I also told him that ppl make mistakes and no relationship is perfect and everyone deserves a second chance but I honestly believe he’s letting his brother get in his ear! What should I do!? Should I keep trying or give him space