I would guess you would fly there, but it would be hard to bring all your stuff. You would probably get caught if you try to recross the border.

The only real bad thing is the 10 yr ban from the US. Also it would be hard to immigrate to other countries since you have broken immigration laws in the US and it would be hard to get a visa there so i doubt it would be easy to study abroad.

I would advise you to stay. Not about anything bad against Mexico, just it would be hard to leave then have something passed right after you leave.