Whilst it is good to go outside your comfort zone occasionally, as it matures you as an individual, it should be your decision. Not that others can not suggest what they think is in your interest, but ultimately you decide.
You say you are uncomfortable around her. Then is there a reason she is your, presumably close, friend?
Have to say I'm not the clubbing type either. I forced myself to go to a few in my youth, but I didn't go a bundle on it. That said, it was better when with friends. I suspect gay specific clubs aren't that different from a meeting folk point of view. It wouldn't hurt you to make the decision to experience a night club, but I'd not hold your breath if I were you. And again it is your decision.
Bye aware there is a benefit to trying to be "out there more", so don't dismiss it unnecessarily. At the moment you can blame your friend for being pushy if you do opt to give it a try; but if they stop encouraging you then you won't have this excuse any more. You don't have to hitch up with anyone, or drink more alcohol than you want.
Give it some thought, maybe consider giving it a try for a few times. But don't rely on it for anything other than a social evening, and don't put all your eggs in the one basket, find other ways to meet folk, that you are more comfortable with.