A couple of weeks ago I got a flat and I wasn't able to replace or patch the tube until today. Now it looks like the tire has deformed after sitting flat on the same spot for so long and comes off of the rim in that area when I inflate it. The inner tube valve also retracts back into the rim whenever I try to pull it out, so maybe it's not seated properly for some reason? What could cause this? I'd hate to have to buy new tires.

Best picture I have: