Based on the pictures, my opinion is possibly an internal tumor. I was expecting something more akin to a tumor or slight bulge, but this is very serious.
I do agree with the epsom salt method. Try bringing him up from 1 tsp/gal to 3 tsp/gal over a 24 hour period. After he's at 3 tsp/gal, do 100% daily changes and redose at 3 tsp/gal epsom salt.
Also, I recommend fasting him for 2-3 days to see if that helps any with the swelling. If it does, he might possibly have a parasite load that he is unable to pass at the moment, which the epsom salt should help with.
If the strand that is coming out of him is white, start immediately on a parasitic medication like General Cure or Jungle brand.
Unfortunately, if he isn't better in 2 weeks maximum or he starts to go downhill fast, I'd say euthanasia is one of your only other options, but give the epsom salt and possibly parasite medication a shot before this.