First off, NEVER EVER put seahorses or other fish that have been in captivity for even a short duration, back into the ocean. They can transfer pathogens picked up while in captivity, into the wild where it can be catastrophic to the wildlife there.
Unfortunately yes, the infection CAN and OFTEN does spread especially when we don't get to treat it very quickly.
Treatment of Tri-sulpha (triple sulfa etc.) and Furan II is NOT something to put on the seahorse, it is added to the water in a hospital tank with heavy aeration from open ended air lines.
I had mentioned this in post #13 with reference to the medication instructions but I will post it again here so you don't have to go looking for it.
It's my experience that a topical med like betadine is great for add on treatment but QUITE insufficient as main treatment for seahorses with bacterial infection. You can keep doing the betadine while doing the treatment of Tri-sulpha and Furan II.
These drugs are NOT normally found at a pharmacy but at your local LFS. (unless you are here in Canada, the UK, or Australia where antibacterial drugs for aquatic pets are no longer available and you have to get a prescription from a Vet.
As MMM said, it IS a bacterial infection and I've not encountered that situation caused by anything other than water quality that allows bacteria to grow out of control, coupled often with temperature above 74°F. NO test kits available to the hobbyist to tell you when the water is getting that way so preventative protocols are required to keep it at bay.
While it is very hard to deal with, you may have to come to terms with the fact it may NOT survive treatment, and when it gets really bad, can't feed and doesn't exhibit signs of wanting to do seahorse things then it is time to euthanize.
Two ways I've used in the past are to put it in the freezer where it slowly shuts down and dies or putting in water with sufficient clove oil to again cause shutdown.