When I learned American English, the rule was that a comma is allways required between two independent clauses. However, my young English friends tell me that they were taught never to put a comma before "and." I think that that rule is altogether too general and really applies only to lists, not to independent clauses, but they take it literally.
I prefer the AE-form with the comma -- it makes the sentence pause where a pause is needed.
Your teacher was probably taught AE, so it's quite likely that it would be corrected. But I can't really forecast that with certainty -- the rules of English are, unfortunately, not that fixed. English is spoken and written in many different countries, and each has developed its own variations. Who is to say which is "correct"? Actually, they all are.