You owe income tax because all money you get for almost any reason is income. You can get tax-free tuition in some cases, but money for living expenses is taxable income.
You may not owe self-employment tax. SE tax is the equivalent of social security and medicare withholding for self-employed persons. In most cases, a graduate or postdoctoral fellowship is not considered "earned income" because you are not "working", you are a student getting an education. (For tax purposes.)
Enter the 1099-MISC in the other income section of Turbotax, do not create a self-employed or small business situation. After you enter the 1099-MISC there is a page of questions, check the box for "this was a scholarship" and then check the box for "No, I did not perform a service" (you were a student getting an education). This reports your fellowship as income, you can then deduct your tuition and fees if you paid them from the fellowship.
See this for more, https://www.irs.gov/pub/irs-pdf/p970.pdf
If your income is less than $31,000, you can file using the Tax Freedom edition, which includes complicated forms not normally included in the free version. It's a different web site for contractual reasons. https://turbotax.intuit.com/taxfreedom/
You must create a different account to use TaxFreedom, you can't use your existing turbotax account. You may also need to clear your browser cache and cookies. https://ttlc.intuit.com/replies/3491786
