Ammonia can burn the gills, and nitrite can prevent the fish from taking up oxygen. But the numbers don't look high enough to cause that much damage that quickly, or to kill the fish in a few days time.
If you have Prime, it will bind the ammonia and nitrite and keep it from hurting the fish. But if your ammonia and nitrite are going up, there is something else going on. Your filtration isn't keeping up with the fish load, or for some reason the beneficial bacteria has taken a hit.
I don't know why the fish died so quickly after you first saw symptoms. What you describe would be, to me, more like flukes that are irritating the fish, not a bacterial infection. But flukes would also not kill them that fast.
If you go to Koiphen.com and ask there, you may find help there. Those are very knowledgeable folks who know much more about diseases than I ever will.
Best of luck with your other fish. So sorry this is happening.