I graduated college in May. I moved to another state and was no longer a dependent, but, my mom paid for my college expenses and loan. How do we file

If you meet either of the qualifications below, you were a dependent. If you weren't, your mother can't claim any education expenses.

Qualifying child

In addition to the qualifications above, to claim an exemption for your child, you must be able to answer "yes" to all of the following questions.

• Are they related to you? The child can be your son, daughter, stepchild, eligible foster child, brother, sister, half-brother, half-sister, stepbrother, stepsister, adopted child, or an offspring of any of them.
• Do they meet the age requirement? Your child must be under age 19 or, if a full-time student, under age 24. There is no age limit if your child is permanently and totally disabled.
• Do they live with you? Your child must live with you for more than half the year, but several exceptions apply.
• Do you financially support them? Your child may have a job, but that job cannot provide more than half of her support.
• Are you the only person claiming them? This requirement commonly applies to children of divorced parents. Here you must use the “tie-breaker rules,” which are found in IRS Publication 501. These rules establish income, parentage, and residency requirements for claiming a child.

Qualifying relative

Here is a checklist for determining whether a relative qualifies.

• Do they live with you? Your relative must live at your residence all year or be on the list of “relatives who do not live with you” in Publication 501. About 30 types of relatives are on this list.
• Do they make less than $4,300 in 2020 or 2021? Your relative cannot have a gross income of more than $4,300 in 2020 or 2021 and be claimed by you as a dependent.
• Do you financially support them? You must provide more than half of your relative’s total support each year.
• Are you the only person claiming them? This means you can’t claim the same person twice, once as a qualifying relative and again as a qualifying child. It also means you can’t claim a relative—say a cousin—if someone else, such as his parents, also claims him.

Since you are no longer a dependent, you may claim the tuition credit, even though someone else paid your tuition.

Although the standard rule in taxes is you must make the payment to get the deduction, education is an exception. 

It's not optional.  Since you re no longer her dependent, your parent is not allowed to claim the tuition credit, on your education.