I don't think you're too young, but like lindahand said, if you're in a commited, long-term relationship, you should discuss with your partner the possibility of him getting a vasectomy, which is much simpler!
If you are looking at something long term, but aren't sure you want to permanently end things you can look at an IUD. Too it is much easier for him to get a vasectomy, day surgery, than it is for you to get your tubes tied - just saying its worth a discussion if you go the sterilization route.
Hi there!
Medically and legally you are not young and you can have your tubes tied, though I would suggest thinking well over the decision since tubal ligation is a permanent method of contraception and can rarely be reversed. You may like to discuss the situation with your gynaecologist.
Hope this is helpful.
Take care!