Filing as married separately would make you ineligible for education credit.
Several things with variations for each of the credits or deduction.
See https://www.irs.gov/Individuals/AOTC
You can use this IRS tool https://www.irs.gov/help/ita/am-i-eligible-to-claim-an-education-credit
Furthermore, 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, 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. You usually must have actually paid tuition, not had it paid by scholarships & 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.