I've recently made the decision to stop drinking. Although I am not an alcoholic, my family does have a history of alcohol abuse, and I am seeing the warning signs.

Whenever I am out in a social situation where people are drinking, I always get asked questions. I don't want to spoil the party by saying I am a problem drinker. Is there a way I can tell people I'm not drinking without demonstrating lesser value? Girls are especially tricky, one HB even offered to buy me a drink because I was the only one in the group not drinking. I refused and I felt myself shrink.

say your the DD
or say you gave it up for lent.
even if its not lent.
theyll be like "its not even lent"
you say quietly "shhh i know but dont tell anyone"
shit like that can get a laugh or two out of them and most likely will avoid the subject all together.
-GL

"Why thank you! I'll have a coke "
Definitely was an IOI, should've just played along. The fact that you don't drink anything alcoholic shouldn't be a problem unless you make a problem of it yourself. Remember, It's perfectly ok to not drink, and if they can't accept that, they're not worth your company.
If they ask, "No really, I don't drink. I see no reason to be drinking, I'm fine with just a coke ".

Honestly, I can speak from experience. I enjoy a good drink at times, and there are times when I actually go out to get drunk with some friends, but I also have times when I just don't feel like drinking, and it's never been a problem.
It's not awkward unless you make it awkward. If you just say "I don't feel like drinking", she'll probably not know what to say, and you'll get an awkward silence. However, if you say that and simply move on with the previous conversation or start a new one, it'll be fine

get a seltzer water and lime.

It looks like a drink but it isnt

And I think you could go two routes with it.

Say things to the target like "man this drink is good you cant even taste the alcohol in it" and than have her take a sip to see if she agrees

or "man this bartender is bad. Theres like no alcohol in this." and than have her taste it.

Most of the time when people are drunk there taste buds go numb and you cant really taste the alcohol anymore. So i think this could work

Good for you for being responsible. Drinking is overrated anyways. Sometimes I feel like drinking and getting fucked up is all people can fucking talk about, the fact that you choose not to drink makes you stand out. And furthermore, I actually think that If someone asked you why, you could say "because there is a history of problem drinking in my family" and that would be find. Its definetly a DHV if you choose to cut out a serious potential problem, just don't let the tone of the conversation veer into party killing mode, keep it light and airy.

I recognise your situation. Im an a frequent drinker as well.
Sometimes girls ask me: why are you drinking water (or something else not alcoholic)

Mostly I say something like:

I have some important decisions to make tomorrow so i have to stay clear.
That demonstrates higher value.
You have more important things to do in your life then getting drunk every evening.