You can't claim yourself if you meet the requirements to be claimed by your parents. Temporary absences while in school are counted as living at your permanent residence so you may still meet the residency requirement but there are other requirements as well if you are under 24. If you are 24 or over and made more than $4050, you can't be claimed by your parents. Whoever claims the dependency exemption for the student is the one who is eligible to claim qualified education expenses paid out of pocket or with loans for the American Opportunity Credit regardless of who actually paid them.
It is usually better for the AOC to be claimed on a parents tax return if the child meets the requirements to be claimed by them.
If you are under age 24 and did not provide more than half your own support from working at a job, you would likely NOT qualify for the up to $1000 of refundable AOC and would only get the up to $1500 of the non-refundable AOC that is offset by your tax liability.