You would not be able to see your parent's tax transcripts without their permission. The request form requires a signature from the taxpayer.
When I worked with the IRS, we were never allowed to disclose sensitive information on the phone so I imagine that is still the policy which would prevent you from calling them. You could send a letter, but I cannot say if you will get a response.
As far as the usage of the AOTC. If you have used it too many times, the IRS will notify you for additional information. Considering you have not received a letter yet, perhaps your parents did not use it.
When the IRS notices a discrepancy in your tax file, they will notify you and if you took a credit you should not have used, they will charge you the difference in what you should have paid plus penalties and interest.
If you do not want to risk it this year you could possibly use the Lifetime Learning Credit if you qualify.
To qualify for the Lifetime Learning Credit, the eligible student (whether it's you, a spouse, or a dependent) will need to meet these criteria:
- The student must be enrolled at an eligible educational institution
- The purpose of enrollment must be to obtain a degree or similar credential, get a job, or improve job skills
- The student must be enrolled for at least one academic period per tax year, which is defined as either a semester, trimester, quarter, or any period of study as determined by the institution in question
