If you are currently in the business of being a writer, then your royalty income from past published works would be included as part of your income reported on Schedule C and subject to self-employment tax.
But, if you are not in the business of being a writer and are simply receiving royalty income for past published works (as it seems in your case), then your royalty income is reported on Schedule E and is not subject to self-employment tax.
The instructions below will guide you to enter the royalties into your tax return if they were reported to you on Form 1099-MISC.
Keep in mind that when you see the question about “Source of 1099-MISC Income” that selecting the option for “Investment income from property you own” will report the income on Schedule E and the option for “Royalty income from your business…” will report the income on Schedule C.
Also, be aware that if you are using TurboTax online, you must use the Premier or Home and Business version in order to report the income properly.
https://ttlc.intuit.com/replies/4792182
To address your question about filing taxes in another state, it depends on the filing requirements for a non-resident of the state where the royalty is earned.
If you are using TurboTax online, you can add the non-resident state return for the royalty income. You should get some guidance as to whether you are required to complete and file the return based on that states requirements and other information from your Federal return. Then, if you are not required to file it, you can delete the extra state without incurring any charges.
Alternatively, take a look at the non-resident state tax authority’s website. The instruction booklet for their individual income tax returns will give the filing requirements for non-residents.
[edited 4/13/2020 | 9:52 am PST to correct typo]
