How can I prove to my parents that I can look after myself?!?

It depends on where in mexico. A lot of drug cartel around the northen part of mexico right now and its really not safe. To get your parents trust you have to show them you are responsible. Do you have a pet or anything? You could try to take of it. Try to spend the night at someone elses house and make sure to be home at your curfew. Call your parents to let them know you are ok. If you take an active approach and show them you are responsible i don't see why they shouldn't let you go out on your own. Unless they are very strict which is unhealthy then you should be able to explore and make your own mistakes.