Swimming upside down or erratically usually means swim bladder issues, but I'm not sure how the skimmer overflowing would cause that in one fish and not all. Antibiotics may help if it is indeed a bacterial issue
Fish is back to normal and eating. Didn't move it or treat it. Just the big water change. I have seen in this hobby before that overreacting is worse than not reacting in most instances where you are not sure of the exact issue.
Doesn't that look like a swim bladder issue to the untrained eye? My knowledge is based on what I read and have seen online or in my own tank. Didn't see a bulge like some fish where they keep floating to the surface, but this seemed quite similar.
Glad your fish is OK. No, that doesn't look like any swim bladder issue I've seen, which usually consists of hyper swimming downward, or swimming in circles. Free floating death moves like what you posted is what I've seen with copper poisoning. I'd assume the same as toxic poisoning from your skimmer.
Moral of the story: If your skimmer craps in your tank, do a water change