Name changes ?

I have had typos on my birth certificate my moms last name and mines. My mom is going to new york city where i was born in july to get it fixed. Should i go with her because what if it the law requires me to be there. She's saying that if i cross i might not be able to come back, but thats better for me because i'll be 18 in august and the border crossing rules are changing. So at least if i stay in the u.s when i turn 18 i can change it myself. That's uming my mom can't get that birth certificate corrected. Once i get a corrected birth certificate how will i get a new ss# in the mail? Would i have to go with her, and why? Her last name was also spelled inncorect so she can't just get it corrected like that. We live in Toronto, Ontarion, and i hear you have to reside in the u.s to get that fixed up. I was thinking of getting my u.s pport with the incorrect spelling so if it doesn't quite work out at least i can styll have something to go back and forth to my country with. input?