If you can't be claimed by someone else and you claim yourself on your tax return, you can enter qualified expense such as tuition and fee amounts paid out of pocket or with loans on your tax return regardless of who actually paid them.
If you can be claimed by someone else, they claim the qualified expenses even if you paid them.
If you had scholarship or grant awards that paid non qualified expenses such as room and board, you enter those on your tax return as income even if you don't claim yourself.
See page 20 in Tax Benefits for Education
Why do you think you don't qualify to be claimed as a dependent?
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. 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.