So I have sort of an opposite problem - I'm 5'9, but I like to bang around the basket, especially defensively - I can guard anyone up to about 6'4 - my guy rarely scores, especially if its a big (my lateral quickness stinks, so I don't want to guard guards) but what happens is b/c of my size, a lot of times people won't let me guard bigs, and I end up guarding a point or a 2 who burns me b/c I can't guard them. Offensively, I like to be the emergency pg, I'm more than happy to let someone else bring it up, but I can help bail people out when needed.
As for your problem of not getting the ball, I'd say A) share the wealth, make the most of your chances and B) if someone is really sucking it up and refusing to pass, you'll be in a new game soon anyways
As for the question of "true point guard" if you are one, I'd be impressed, as they are few and far between whether on the playground, the hs court, college, even the NBA.