A Slip Up

Ended with my girlfriend after six months because we just weren't on the same page anymore. We decided to keep things civil but... last week, I slept with someone else. It wasn’t supposed to happen like this, especially not when there was a mutual friend in the picture too. Now every time I see her, even from across a crowded room, my heart starts pounding and I feel sick. Should I tell my ex? Do people really do things like this after breakups or am I just some kind of monster?