You can report self-employment income without Form 1099-MISC.
When you reach the screen with the image of a 1099-MISC that asks if you received this form, say "No" and continue. The program will give you a place to record all income received that was not reported on 1099-MISC.
This is totally acceptable to the IRS. The burden to report on Form 1099-MISC lies with the payer, not the contract worker.
The easiest way to get to this screen is to use the Search box for "1099-misc" and click on the "jump to" link.