i've had glasses for a long time and now a while ago i switched to contacts and when i was at the opticians i saw probably a 3rd grader gettin contacts, very young, and very whiny
ofcourse after he got the test ones in he started crying because they were bothering him when he didnt even give em time to get used to it and later i heard when i was in the chair waiting i heard he wants glasses back. Glasses are easier and less harmful to your eyes but contacts are more comfortable (for me). I myself wear 2 weeks ones and i usually wear them 3-4 weeks, until they start to blur out
To answer your question then yes, 13 year olds can wear contacts
EDIT: i got contacts because glasses bothered me when i did sports and sometimes i had to remove my glasses and then i couldnt see, but now i can see clearly and im happy for it
so if you just want contacts for no reason then reconsider because contacts are more harmful to your eyes than glasses as i mentioned in the rant above, and btw glasses dont make you look stupid, its you who thinks glasses makes you look stupid and if people make fun of you then mind them, just let it go, do what you want as long as you feel comfortable with it