Caught lying

Yesterday, I screenshot a conversation me and my boyfriend had so I could remember it. Last night, he looked at my phone and said "why did you screenshot that".

I was slightly drunk and really embarrassed that I did that so I lied. I said "oh I accidentally did it and then I cropped it so I could remember it because i delete my texts".

First, I don't delete my texts and second that was just a plain lie. He said "that doesn't sound like the truth and then I waited a minute before telling him the truth that he just was being nice and I wanted to remember that.

This was in the car driving home. When we got home, I asked if we could talk and I told him that I really cared about him and that I don't like lying. I apologized for doing it and said that I didn't want to start down a path where we are both lying or even one of us. I told him that I didn't want to loose his trust. I also told him that I was embarrassed to tell him the real reason because he is not emotional so I feel that I have to be that way too. He said it's not a big deal and that he just wanted to know the truth but I know that I messed up. I told him that I would be mad if he lied to me and he said "good thing I didn't".

(He has lied once before about me finding pink socks in his house but that's not the point)

Can you girls tell me how bad it is? I woke up feeling so guilty my stomach dropped. Do you think it's a deal breaker? I truly care about him and I can't believe I did that (even though I was drunk). Would apologizing again today be too much? I feel awful and I really do hate lying. Did I ruin his trust forever? What do I do?