The UC exclusion worksheet makes my income $0. So Turbo Tax says I can't file elctronically because my tax withheld is more than my income. Do I have to file by paper?

Not really, what you can do is to create a 1099-INT, as-if from your local bank...and put $1 of interest in it.

If you DO actually have a bank account, use that bank's name.  You may have actual interest from that bank.  They don't issue a 1099-INT if it was less than $10, but you should report the interest you received  if it is at least 50 cents.   But at least a $1 creates potentially-taxable income that allows you to e-file.

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If you removed any $$ from an IRA, or other retirement account, make sure you enter that 1099-R too....and don't forget any W-2 forms you should have received...IF you were working a W-2 job before the shutdown.  Don't depend on the software "knowing" what income you have to enter.