Where do I input the Cost of Goods Sold for self-employment? I cannot find it in the deductions section in my return.

You would enter it in the Inventory part of the Self-Employment section of the interview, which is just after the Income part.

I do not have this section. Is it because this is a partnership business? Or did I not choose something else correctly?

When began entering in your self-employment/business information, did you choose "Professional" as your category type? If so, you won't see anything regarding cost of goods sold or inventory, as "Professionals" generally provide services, so they would report work-in-progress instead.

Unfortunately, there is no way to change the category type once you have reached the “Your Self-Employment or Business Summary” page. You would have to select Income > Self-Employment > Self-Employment Summary from the left side menu, then delete the business & recreate it with the Business category type.