I got drunk and made a bad impression, do I still apologize?

My parents wanted a better life for me long ago, bringing me to Maine. I was 3 years old at the time. These people we're friends with have known us for the longest. They have/had (they probably think something differently now) a good impression of me.

I've been exhausted with exams lately and got drunk with a couple new college female friends. They've been trying to convince me for the longest to not take things too serious, relax and enjoy life. I finally gave in, went to their party and we (including me) got all drunk. This isn't the first time drinking but I've never drank a lot before; not like that.

I obviously came home very drunk, walking sloppy, suddenly saying a bunch of nonsense (mocking god and other things) and starting vomiting. I think they were shocked that was coming from me. I've just made the one of the worst impression aobut me. Do I apologize though?
I got drunk and made a bad impression, do I still apologize?
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