It depends. This type of situation is not always clear-cut. You could be justified in claiming this as other income if there is no true profit motive for the work. In this scenario, the amount of deductions you may claim for the income is limited to the amount of other income (hobby income) earned. In addition, they form part of itemized deductions up to the point of where the amount deducted exceeds 2% of your AGI. Other income is generally not subject to Self-Employment tax.
Self-employment is subject to self-employment tax, but you can claim the full amount of expenses you paid (mileage will be a significant part of this, even though you were partially reimbursed and would include the reimbursement as income to be able to fully deduct the expenses). Self-employment can suffer a loss, but losses year after year can cause the IRS to recharacterize the endeavor as a hobby, which forces the expenses to be limited as I describe above.
Here is an IRS website that provides additional information on this subject: https://www.irs.gov/uac/newsroom/five-basic-tax-tips-about-hobbies. You will have to make the choice as to which is the correct status of this income. Make sure that you have documentation in your favor if the IRS questions the choice.
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