i would just continue playing at the field and over the next couple years get your parents involved a little more. if they don't watch you play? ask them to take pics of you or something.. start conversations about paintball during dinner. do anything you can to mention paintball, but don't push them. once you are a little older they might loosen up a little.
it sounds like you really want to make some progress and thats AWESOME. but, at your age, parents tend to control you the most cuz right now your at a stage where every decision you make will affect your future. and they know that. so they are going to control your life quite a bit. (my dad is a Colonel in the Air Force so i know everything about this
but in the mean time, let the team captain know about your situation and tell him you would like to play in the near future. and while your waiting just keep practicing. your time will come