It's called "oil canning" (like the bottom of an old oil squirt can)....
No -- I would not weld the area...
The stretched metal can be dolly and hammered -- or shrunk using heating and cooling the area.
Trust me on this - this is no place (on a freshly painted panel) for a beginner to learn to shrink metal. Take it to a QUALITY body shop and have it fixed. Or leave it alone.
Sorry to hear you had the issue... but really -- shrinking metal correctly is a learned skill... and needs to be done but someone that knows what they're doing otherwise you're going to end up with a huge mess... creating more problems than you can solve.