Hi Anny, welcome. I'm new, too.
I don't know NY's penalty for underage alcohol consuption/buying, but I wouldn't risk finding out the hard way. Your girlfriend is only understandably anxious about the risk of buying you a shot, but maybe you could sneak a miniture into your glass when nobody's looking.
I used to do that when much younger, when dad wasn't looking. Even sneaked some vodka into a small bottle of mineral water, but shh! You didn't hear that from me.
Age gaps don't matter when you're in love, so I say go for it and ignore those you know in your home town saying otherwise.