"How do I make a J/E with a CR to Owner's Draw and properly record it in COG Sold? I am using QBO Adv. I bought items with my personal money that were sold to clients."
Instead of writing a Journal Entry, you may want to create a Zero Bill (Left dashboard > Vendors > Bill) in QBO. This works far better for tracking both Vendors and Customers. Checking the Billable box is optional if you need to Invoice only.
See the screenshot below for reference.