I hate to sound like a jerk, but consider this: if your parents have already expressed their discomfort with you getting a hotel room, how would they feel about the fact that you are not only denying their wishes with no clear motivation as to why, but you are also expecting complete strangers on an internet forum to accommodate you? :/ It would do very little to change their minds.
If you have never stayed at a hotel before and never been to a con for a whole weekend before, it is unwise to commit yourself to the whole 9 yards straight away, and I'm not sure why you're even considering it if you already know the money is not there. Start by going to cons for 1-2 days that you can travel back and forth to with reasonable ease. I started cosplaying at your age and I didn't start doing hotels for full weekend cons until I was 19. Hotels are booked for comfort and necessity, not necessarily because they look fun and glamorous. If you are trying to prove to your family, other people in the cosplay community, or even to yourself that you are responsible, this is not the way to do it. If you're really committed to this, find friends or peers in your age group (including at least ONE legal adult willing to be a guardian for the weekend, since you will need one present for hotel booking and sign-in), and get everyone to save up the money, and make sure they take the commitment seriously.