Should my self-employment income also be reflected in 1099-MISC income? Since it's using the same 1099 forms in both places, is it double reporting?

If you are self-employed and the 1099-Misc is for income received for self-employment, you only enter it in the section about your business income.

There are other types of 1099-Misc that are entered as 'other taxable income' but this does not apply to you.