I started graduate school in August of 2023 as well. I've only claimed the AOC once, and I didn't complete four years of college at the beginning of the tax year (January 1, 2023), so why don't I qualify?
The AOC is for students who have not earned a bachelor degree yet. It can be used for up to four times during your undergraduate years, but now that you are a grad student, you cannot use it. Instead you can try to use the Lifetime Learning Credit. The LLC is non-refundable---it can reduce your tax owed, but is not added to your refund.
https://ttlc.intuit.com/questions/3262984-who-is-eligible-for-the-lifetime-learning-credit
Graduating college in 4 years usually means you were in college 5 calendar years. There is a 4 time limit on claiming the American Opportunity Credit (AOTC). If you, or your parents, already claimed it in 2019, 2020, 2021 and 2022, you can not claim it in 2023.
Otherwise grad students are eligible for the AOTC, in the year they completed their undergrad degree. You may count both the grad & undergrad expenses for the AOTC. You may not claim both the AOTC (for the undergrad) and the LLC for the grad.
If you qualify, go back and check your interview answers, particularly the one about completing 4 years of post secondary education. If that fails, delete the education and start over.*
*Go through the entire education interview until you reach a screen titled "Your Education Expenses Summary". Click delete next to the student's name. You'll then get the "Your Education Expenses Summary" screen again. Click the "Add a student" button. You'll have to manually re-enter the info.