If I’m in cosmetology school and used financial aid, can I file it as a college course?

Maybe.  Is the school accredited?

If you are someone else's dependent the person who claims you as a dependent is the one who can get the education credit.

https://www.irs.gov/help/ita/am-i-eligible-to-claim-an-education-credit

https://ttlc.intuit.com/questions/1901172-what-are-education-tax-credits

https://ttlc.intuit.com/questions/1901487-what-is-the-tuition-and-fees-deduction

https://ttlc.intuit.com/questions/1901172-what-education-tax-credits-are-available      

https://ttlc.intuit.com/questions/3262983-who-is-eligible-to-take-the-american-opportunity-tax-credit

https://ttlc.intuit.com/questions/3383321-why-didn-t-i-get-a-credit-or-deduction-for-education-expenses

Yes, vocational schools are eligible. But, to be eligible for the tuition credits or tuition & fees deduction, the course must be taken at "an eligible institution". The school should be able to tell you if it is an eligible educational institution. In general, an eligible educational institution is an accredited college, university, vocational school, or other postsecondary educational institution, including accredited, public, nonprofit, and proprietary (privately-owned, profit-making) postsecondary institutions. Additionally, in order to be an eligible educational institution, the school must be eligible to participate in a student aid program administered by the Department of Education. If they issue a 1098-T they are probably an eligible institution.

Enter your school at the link below, to see if it's on the dept. of education list.

https://fafsa.ed.gov/FAFSA/app/schoolSearch?locale=en_EN

Probably, with some "buts".

The school must be accredited by the US Dept of Education to participate in student aid programs, and the school must issue a 1098-T.  It sounds like you did get aid, so you just need to make sure the school will issue a 1098-T.

You must determine if you attended school "more than half time" as defined by the school.  If you attended less than half-time, you are eligible for the lifetime learning credit but not the American Opportunity Credit.

You must determine if you have attended a higher education program for more or less than 4 years.  If you have a 4 year degree (even if you got it in less than 4 years) or if you have already attended a school of higher education for 4 years (even if you did not get a degree) then you are eligible for the lifetime learning credit but not the American Opportunity Credit.

Look at your expenses.  There are 3 kinds of expenses that might be eligible depending on the kind of credit you are eligible for.  (1) tuition and required fees you pay to the school.  (2) supplies that are required for your program of study that you must buy from the school, and (3) supplies that are required for your program of study that you can buy elsewhere.  You can't claim any credit if you did not pay for the  expenses with your own money or a loan in your name.  

When you enter your 1098-T, Turbotax will ask you all these questions -- were you more than half-time, have you already attended 4 years or more, what were your tuition expenses, what were your supply expenses bought at school, and what were your supply expenses bought elsewhere.  Turbotax will then determine which credit you are eligible for, and if you are eligible for more than one, it will claim the credit that gives you the largest refund or reduces your tax the most.

In some cases, if you got free money (like a Pell Grant) that was more than your tuition and fees, that you used for other living expenses, that will be taxable income instead of giving you a credit.