Schedule C is the correct place for that type of income.
Although it may be news to you that you “have a business” (and most of the other people who get their first 1099-MISC); The IRS considers anything in box 7 of 1099-MISC to be self employment income. Even for 16 year olds! Enter the 1099-Misc income, at Other Common income / income from a 1099-MISC . TurboTax (TT) will complete Schedule C or C-EZ for you and allow you to deduct any expenses associated with this income. You'll also have to pay self employment tax (social security & Medicare) on any profits greater than $400. These types of payments are frequently done this way. Your "employer" is not the only one.
