For right now, I say tell them what is comfortable for you, but beware of weaving a web of lies, which can be much worse than being upfront.
For me, I was also embarrassed at first, I felt like people were watching or judging me (I learned later they weren't). For the first year I told people I stopped drinking to focus on parenting (I had a newborn at home), it was enough of the truth it usually never went past that.
These days (3 years later), I'm proud to rock the fact I don't drink. I feel like I have this put-together on-top-of-everything identity, and I credit it to not drinking. In my experience, most people do not care if you drink or why you're not drinking (it's all in your head).
But it did take a year or so to become comfortable in my own skin and not feel like I had to make excuses for not drinking.
Good for you and keep it up :-)