Why did a bulge appear after I mounted a wine rack to my wall?
You have a textbook screw pop there, where the drywall hanger didn't run the screw in snug, leaving a gap behind the drywall. When you mounted your rack, the drywall was pressed tight and the protruding screw forced the surface out.

The fix is do drive the screw in (through the joint compound) and repair the damage. Even if you remove your wine rack the outline of the bulge will probably remain visible. 

Fortunately, you have smooth walls. I'd pull down the rack, run the screw in tight (remove it or drive it through with a hammer and set if it spins free), cut out the loose material, and skim with drywall joint compound. It will probably take several applications, with dry time in between, due to shrinkage. Sand, paint, and hang your rack again. 

Of course, you could also drive the screw in, then raise your wine rack a bit and pretend it never happened. :)