@CreativeAddiction
OK, while the boys are all duking it out.....
I think the biggest issue is of water quality, no matter what the cause. Yes, that is WAY too many fish for that size pond, despite water overflowing, or rain, or just whatever.....
As one mentioned, are you certain of the size of the pond?
Your fish are producing more waste than your filter can handle. (See link below for a fish load calculator -- it might give you some insight). This stresses the fish. Remember that they breathe through their gills, so what's in the water (ammonia, nitrites, any other toxins) is what they are breathing. That's why they are gasping at the surface for air. It would be the equivalent if you were to walk around in an inclosed room full of toxic air, say a burning building -- assuming the heat didn't get you first, you would quickly be overcome by the smoke & fumes.
YOU can walk out of that burning building, but your fish CANNOT get out of THIER toxic water. It's up to us to keep their water environment as clean & livable as possible. So put out the fire, open the doors & windows, and turn on the fans -- get the smoke & fumes outta there QUICKLY!
Your best options are to add more filtration, more air, more surface agitation, very frequent water changes, and reduce your fish load!
http://www.your-garden-ponds-center.com/fish-load-calculator.html. Here's a fish load calculator that might help.
Get a water test kit (liquid, drops kind) and check your water -- keep a log. Learn what to watch for and watch for those changes.