There is no credit just for being a full time student. There is a credit for having paid certain higher education expenses.
If you are eligible, you have answered something wrong, in the interview. But, a lot of people are just not eligible. See https://www.irs.gov/Individuals/AOTC or https://www.irs.gov/individuals/llc
It may only be you are looking in the wrong place. The non-refundable portion shows on line 33 of form 1040A (line 50 of form 1040) and will be blank if you had no tax liability to off set. The refundable portion (up to $1000 will be on line 44 of 1040A (line 68 of 1040).
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 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 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. There is a limit of claiming the AOTC a total of four times (4 tax years) per student, whether claimed by the student or his parents. You cannot file as Married Filing separately.
Go thru the interview again. In particular, Edit your personal information at the beginning of the software. When Turbotax (TT) sees from your birth date that you are under 24, it specifically asks if you provided more than half your support with earned income.
Also see this TT FAQ https://ttlc.intuit.com/questions/3383321-why-didn-t-i-get-a-credit-or-deduction-for-education-expen...
