Petty Lies and Lost Trust

I recently got separated from my college sweetheart, and I feel like all trust between us is shattered. The thing that did it was something so small, I lied about picking up groceries last week when I really just wanted to get out of cooking dinner. Instead, I went home with a friend who offered me a ride after class. There wasn't anything romantic or sexual in our interaction; we just hung out and talked until late. But the next day, when my ex asked if I'd gone grocery shopping, I lied because I knew she'd flip her lid at the thought of being alone in public with someone else. Now every little thing is blown way out of proportion. I know it's a silly reason to lose everything over, but it feels like this lie has created an insurmountable rift. Maybe I should have just been honest, we've had bigger fights before about nothing and made up easily. But now it's too late.