Day 6 post Gastric sleeve, what do I do with the Cotton in Belly button?
I would ask your medical team. The thing I'd be concerned about is that the cotton ball might be stuck to a scab, and if you pull it out there's a chance you might re-open a wound and expose yourself to infection.
I'm not advising you to do this, but if you're determined, maybe gently and slowly pull on the cotton ball to see if it is stuck to anything. If it comes out easily, that's grand, but if you feel that it's stuck, call your surgeon's office. They might want you to come in, or they might suggest you dampen the cotton ball with warm water and remove it yourself, keeping an eye out for bleeding.