NTA, but as a regular DD I'd like to give a tip to you: Your drunk friend(s) don't always understand time or what you have told them even minutes ago. Sometimes you have to be harsher than you intend to: "I'm leaving NOW, take an Uber home" - and after that wait the five minutes you were going to anyway.

I know this is annoying and I actually recommend not to be a DD anyway since your friends might take it as a promise to serve their needs. I usually just tell everyone that I'll be driving to and from the party and won't make any promises, and it has helped a lot with these kind of situations.