If the dollar amount reported to you is in Box 7 then, by definition, you have a "business" even if you don't consider it as such and that income, (and any related expenses), need to be reported on Schedule C. Don't report the 1099-MISC in the stand-alone "1099-MISC" interview, simply start the Schedule C interview and enter the information over there, along with any legitimate expenses.
"My question is this - when I put in the amount I was paid in both the 1099 area and the Schedule C - my taxes go from a refund to me paying. I feel like I'm missing something as to how to make this work."
You probably are entering the income twice but trying to judge the correctness or otherwise of your income tax return by looking at the "Refund-O-Meter" at the top of the screen is simply wrong. When you feel that you've entered all the required information for your income tax return print out your income tax return before you file and check it for accuracy. Only when you're convinced that you income tax return is as correct as you can make it, then you file.
