Question

How do I manually add prize winnings if I didn't receive a 1040-misc?

When I try to add in that section it asks me if I received a 1040-misc and when I say no it just puts me back to the main income section

I would report as "Other Income". To do so, while logged in to your return:

Click on Federal
Click on Income & Expenses
Scroll to the bottom of the "Your income and expenses" page, and click on "Less Common Income"
Click on "Show more"
At the bottom of the page, next to "Miscellaneous Income..." click on Start/Revisit
Other reportable income - click on Start, then answer Yes
Give a description and enter amount of income from the prize winnings