how much pda is too much in high school for a gay couple?

Most people don't know that my girlfriend and I are dating, or that I'm a lesbian and she's bi. We put our arms around each other and hold hands mostly, but sometimes she'll lean against me or we'll sit on each others laps, etc. We're going to prom together, so I think people will start to realize we're together then, and I think that will make a difference (as girls can be physical like that with one another without being gay, but once they know we're dating they'll see it differently).
Also, is it normal that we've been together for almost a month now, kissed three times, and not gone on a date yet? This is my first relationship ever so I'm clueless.

(I'm 16 and she's 17 btw)
@Anonymous: I would like to, but I've been busy the past weekends and the weekend after next is prom, which is a date anyway. My dad wants her to come to dinner with us (he doesn't know we're dating but knows we're going to prom together) but I feel like that would be incredibly awkward and I'd much rather do the typical movie date.
We've kissed at school, but in private. I wouldn't want to start making out randomly with anyone in public, especially at school and with another girl. Awkward for everyone.