I work at a shelter and have been involved with every shelter in this area at one point or another. Each one has its own individual rules but I haven't come across one yet that allows 13 yr olds to come without a guardian. Most shelters you have to be either 16 or 18 or otherwise have a parent or guardian with you. There's too much liability with the animals and also without supervision could become crazy. I know you're responsible but unfortunately rules are made for the minority of immature people.

Hopefully your parents can go with you on the weekend. Its a lot of fun and you'll be doing a world of good. Good luck