You can only claim one education tax credit per year per child.
AOTC can be taken for four years, it allows books to be qualified expenses as well. The first $2,000 of QEE result in $2,000 of AOTC (if you have tax liability, up to 40% max $1,000 can be refunded).
There are income limits for the AOTC as well.
If you have a 529 account, room and board are qualified expenses for tax free 529 distributions.
But no, you cannot get $2,000 AOTC and then try to claim tuition and fees deduction on the same tuition expenses for the same year/child.
The max AOTC is $2,500. So you are pretty close with $2,000. If you haven’t included books, you can claim them in addition to tuition/fees listed on 1098T.