No, that limit is for state tax.
You claim state tuition expenses differently than state tax.
You should have received Form 1098-T showing the tuition paid in Box 1 and any scholarships received in Box 5.
Enter this information under "Deductions and Credits" Education.
Go through the ENTIRE education interview and answer the questions carefully.
If the expenses paid are more than the scholarships received, you won't get a deduction on Schedule A like a state tax paid, but you may get an education credit.
The TurboTax program will tell you if you are eligible.
Contributions to an education savings account is reported on your state return.
Some states offer a state credit for those contributions.