Platy With Frayed Gills

Two days ago I noticed the lower edges of the gills on my sunset platy looked a bit frayed and were sticking out slightly.  She seemed fine otherwise so I have been keeping an eye on her.  The gills look the same and today she is hiding and will not eat.
 
What is wrong with her?  What should I do?

Are you certain what you are seeing is frayed gills and not something else? Have you seen the fish flashing against objects in the tank?
 
I am wondering about the possibility of gill flukes.

Thanks TTA, I've not noticed any excessive flashing. 
 
Here is a picture I got of her when I noticed the abnormality a couple of days ago
 

Is it the gills or the gill plate? I am assuming the problem is on the left side?
 
Could that be a bit of fungus? Its hard to tell from the pic.

Sorry it's really hard to get a pic!  It looks like both gill plates (operculum?) are curling outwards slightly at the lower edge.
 
I was worried it might be fungus at first too but I think not.  I can't be sure.

It is hard to diagnose remotely. Have a read here and see if this might be it. http/www.fishdoc.co.uk/disease/costia.htm
 
Flukes you can spot with magnifying glass, Costia require a microscope.
 
Yes - operculum. I am a member of the ego odi Latine club (aka the Abhorreo Latinam Assn.).

She came out for some food today but has mostly been hiding again.  I noticed what looks like a couple of pale patches on her flank.
 
Should I move her to a hospital tank and treat with salt?
 
I thought my water quality was okay but perhaps this problem is somehow caused by overcrowding due to the sheer number of fry in there.  I've been busy setting up a new fry tank and I will move some of them out tomorrow.

Its is easy for the arrival of fry to sneak up on you. They start to grow and suddenly their ammonia output is higher than realized- but testing should catch that.
 
I can't recall what diseases might cause patches and gill related issues. I am lucky in that my disease experience is somwhat limited on a 1st hand basis. I often rely on more expert folks for help myself. The things i have treated i know, the ones I have not i only know about or where ti find out about.
 
It is also possible you are seeing two different things. Salt wont help with ammonia only nitrite- or fungus and certain external parasites.
 
Its the operculum issues that bother me. I would treat the tank for flukes- QuICK Cure or Prazipro- to be sure.
 
For QuICk Cure- Do not use on: baby whales, elephant nose, shrimps, snails, living rock or invertebrates. Prazi is the way to go bu more money.
 
Salt dip would kill fluke on a fish but not free swimmers in tank- think ich like.

Thanks for the help TTA.
 
I moved 10 of the largest fry out of the tank yesterday and rehomed an adult female who was about to give birth to yet more fry.  Spicy has perked up immediately and is much more active today although her gills still look the same.  I will add a bit of salt to the tank and look for fluke treatments (I don't want anything that will harm inverts, I was hoping to get shrimp in the next few weeks)!