A single member LLC is defaulted to a sole proprietorship by the IRS for tax purposes. You will file a Schedule C and Schedule SE attached to your 1040. TurboTax will ask you the appropriate questions to fill out the form when you indicate that you have self-employment income.
You can check with the Texas Workforce Commission here how the timing of the payments you received affects your unemployment. They have a chat feature: https://www.twc.texas.gov/programs/unemployment-benefits
Congratulations on your new business! Here is a great resource for small business: https://turbotax.intuit.com/tax-tips/self-employment-taxes/beginners-tax-guide-for-the-self-employed...
Hope this helps!
Cindy
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