Nothing you have said (NJ resident, school in PR) would disqualify you from claiming the AOTC. But, there's more to it than that.
There's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. It is usually best if the parent claims that credit.
You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.
Reference: Line 7 instructions for form 8863. https://www.irs.gov/instructions/i8863
See Also see this TT FAQ https://ttlc.intuit.com/questions/3383321-why-didn-t-i-get-a-credit-or-deduction-for-education-expen...
Other references:
https://www.irs.gov/Individuals/AOTC
https://www.irs.gov/newsroom/american-opportunity-tax-credit-questions-and-answers
https://www.irs.gov/credits-deductions/individuals/education-credits-questions-and-answers
https://ttlc.intuit.com/community/college-education/discussion/i-have-a-1098-t-form-that-i-received-...
