Your part-time income would be reported on a tax return as 'Self-Employment Income' which is why TurboTax is asking you to upgrade. You can report the income and also some related expenses.
This could make you eligible for the Child Tax Credit and possibly the Earned Income Credit.
You may want to check out the IRS Free File Program to file a return for free.
If the income you earned from working is less than $3000 you are on the edge of not being eligible for the refundable additional child tax credit. You need at least $2500 of income from working to get any thing added to your refund. You get 15% of the amount over $2500 added to your refund. So that is very little.
You might also get a small amount of earned income credit.
But----you have self-employment income which is why it says you have to upgrade. You cannot put self-employment income into the Free Edition.
Use this IRS site for other ways to file for free. There are 8 free software versions available from the IRS Free File site
https://apps.irs.gov/app/freeFile/
Or—if you live in certain states you may be eligible to use the new IRS Direct File
( AZ, CA, FL, MA, NH, NV, NY, SD, TN, TX, WA, WY )