There are worse things than obeying the law, and I can understand the authorities not having teenagers barfing in the gutters they way they do in Britain, and I can understand your partner not wanting to get into trouble. However...
Just what is it you want to do exactly? I can appreciate that sipping Diet Coke while everyone else is chugging beer must be frustrating. But do you actually want to be 'drinking heavily' as you say others are?
And while I don't doubt you're in love, I can't help wondering if your partner isn't behaving like your mother? And if maybe this isn't niggling at you a bit? After all, there's nothing (except the law!) stopping you buying your drinks yourself; she doesn't have to do it. And yet quite apart from whether a barman would serve you, *she* won't 'let' you do it. It strikes me this isn't quite an equal relationship, is it? How do you feel about that?
Anyway, you can suck it up; or you can suggest you don't go out together until you're of age; or you can simply refuse to go out with her whether she likes it or not; or as a last resort you can find someone your own age who'll feel a bit more sympathy. Up to you to decide what you really want, deep down.