I got hired on as a teacher but am paying for my alternative teaching license/classes as I teach. Required as part of the job. Can I claim tuition/fees? No 1098-T form.

You can not claim a tuition credit or the Tuition and fees deduction on line 34 of form 1040 (line 19 of 1040A), because it is not an eligible institution.

However the expenses are deductible as a job expense. You are allowed to deduct your tuition and fees and other job expenses, subtracting what you were reimbursed (do not subtract your reimbursement if it was included on your W-2 as taxable income). TurboTax completes form  2106, which  then carries to Misc itemized deductions on Schedule A. The problem with this is that you only get to deduct that portion of  your misc deductions that exceed 2% of your AGI. and then only if your total  itemized deductions exceed the standard deduction.  (2% rule explained: https://ttlc.intuit.com/questions/2902781-what-is-the-2-rule)

 In TurboTax, enter at:

Federal Taxes Tab

Deductions & Credits

I'll choose what I work on

-Scroll down to:

-Employment Expenses
-- Job related expenses

You can also deduct the mileage if you go directly from your work site to the school. You cannot deduct the mileage from school back to home, unless the schooling is considered temporary (expected to last less than 1 year and actually does last less than 1 year).