Will I get any kind of credit for being a full time college student last year? I graduated in September

You may qualify for an Education Credit. While the American Education Credit is only for the first two years, you may still get the Lifetime Learning Credit.

Who can claim the LLC?

To claim the LLC, you must meet all three of the following:

1. You, your dependent or a third party pay qualified education expenses for higher education.
2. You, your dependent or a third party pay the education expenses for an eligible student enrolled at an eligible educational institution.
3. The eligible student is yourself, your spouse or a dependent you listed on your tax return.

See "Who Cannot Claim an Education Credit" on our Education Credits — AOTC and LLC page.

Yes, at least in some way.

The more generous American Opportunity Credit  (AOC or AOTC) is good for the first 4 years  (not 2 as the other post said) of post secondary education and may only be claimed 4 times.  Graduating in September usually means 2022 was your  5th year of undergrad work and your parents probably already claimed the AOTC 4 time.  So, you, most likely cannot claim it. As the other answer indicated, you probably qualify for the LLC.  Too much scholarship or having a 529 plan might limit how much, if any, LLC can be claimed.

Next comes the question of do you claim the LLC or do your parents.  If you can be claimed as their dependent, you can not claim a tuition credit. 

Can the student be claimed as a dependent in the Graduation year? (answer written as if the parent asked the question)

If he/she was a student (under 24) for at least 5 months and lived with you for more than half the year, and did not provide more than 1/2 his own support for the whole year, you can still claim him. Be sure he knows you're claiming him, so he doesn't claim himself. He can only be claimed once. But, he can "file taxes" without claiming his own exemption.

The real question is who should be claiming him in this "transition" year to adulthood. You two have to agree on who is going to claim his exemption. Each should do their taxes both ways and see which way the family comes out best.  Even then, you have to meet the rules. 

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit.

The rule is that a child of a taxpayer can still be a “Qualifying Child” dependent, regardless of  his income, if:

1. he is a full time student under 24 for at least 5 calendar months of the year (graduating in May usually means you meet the 5 month rule)
2. he did not provide more than 1/2 his own support  (scholarships are considered 3rd party support and not support provided by the student). 
3. lived with the parent (including time away at school) for more than half the year

So, it usually hinges on  "Did he provide more than 1/2 his own support in 2021.

The support value of the home you provided is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants. IRS Publication 501 on page 20 has a worksheet that can be used to help with the support calculation. See: http://www.irs.gov/pub/irs-pdf/p501.pdf  (page 15)