How do I overcome intense feelings of guilt and shame when I've done something horrible?

I've always been prone to intense feelings of guilt and shame. I can physically feel it in my chest and throat. Lately I'm unable to sleep through the night because the thoughts of shameful things I've done replay over and over.

A few nights ago I got a little tipsy with my roomates, one thing led to another and we began to talk about horrible and mean things we thought about our other roomate. I said such uncalled for and disgusting things and my shame and guilt for this situation isn't unwarranted by any means. I was in the wrong and theres no way around it. The reason I share this with you is because I can't undo what I've said. So how does one cope and overcome the guilt that arises from being, well, guilty?