You say it's in QT, yes? What is your water chemistry like? Ammonia, 'trites, 'trates, and pH readings?
It's a good sign that she's eating. It's still very tough to tell from those shots...can you get some better ones? From your description, I don't think it's ich, but I can't give you any firm answers..just some best guesses. Tissue necrosis is a generalized term for any bacterial infection that causes tissue death and erosion. For example, snout and tail rot are types of necrosis usually caused by Vibrio infections.
Is she (it is a she, yes?) using the fin regularly, or is she keeping it clamped down against her body a lot? Fin rot is a known condition in seahorses, and from your description sounds like an issue she might have. Fin rot is considered a little less threatening than other necroses for our horses, but still something that needs to be taken seriously. Fin rot can be cause by a number of different bacteria that lie semi-dormant both in the tank and on the horse. These bugs typically start to get out of control when the animal is stressed (a move to a new home, for instance!) and when water quality is poor....which brings me back to my earlier question about the Big 4 for your water chemistry.
If your parameters are out of whack, I'd recommend at least a 50% water change. Even if they're in line, I'd still do at least a 25% water change every couple days. Lower the water temp to 70 if you can by putting a fan over the top if you don't have a chiller...this will slow the bacterial growth and give her time to let her natural defenses take over. And by all means, WATCH that fin. If it's getting worse, you may need to use an antibiotic, but I wouldn't do that just yet....remember, I'm going off of some guess work here from your description and could be DEAD wrong.