Mileage for what? You cannot claim the mileage from your home to a school (or school to home) --that is commuting which you cannot use. If you drive between schools during the school day, you can use that mileage on a Schedule C as a business expense.
Will the school district be giving you a 1099Misc instead of a W-2? If so, you are indeed an independent contractor.
https://ttlc.intuit.com/questions/2893577-does-a-1099-misc-mean-i-m-self-employed
https://ttlc.intuit.com/questions/2902389-why-am-i-paying-self-employment-tax
https://ttlc.intuit.com/questions/1901110-do-i-need-to-make-estimated-tax-payments-to-the-irs
https://ttlc.intuit.com/questions/2903027-how-do-i-report-income-from-self-employment
https://ttlc.intuit.com/questions/3398950-what-self-employed-expenses-can-i-deduct
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