What type of disease is this?

[victoriamz17]

Background—I work at a local pet store in the pet care department. I have had fish tanks for years and have experienced some diseases, but not all. We had a sick female betta with lesions on her dorsal fin which the store manager treated with bettafix for a week straight. He claimed the lesion was not shrinking and may even be growing. The betta seemed to be swimming well and didn’t appear to be uncomfortable. We are unable to sell sick/deformed fish so he put her up for adoption. Not wanting her to go to an inexperienced home, I chose to adopt her. Since having looked her over, it appears she may also have lesions on other parts of her body. I tried to get decent pictures and have uploaded the best ones.
Current set up—I have a 0.5 gallon heated (not filtered) tank I use for isolation and treatments. When I brought the betta home, I removed the gravel and rinsed the tank before refilling it with purified (by reverse osmosis) water. I acclimated the betta as I always do new fish (first floating the cup in the new tank, next adding some tank water into the cup, then netting the fish and placing her into the new tank without mixing the old water into the tank water).
My question—Does anyone have an idea what this may be? I thought maybe it’s a fungal infection and started Melafix/Pimafix treatments. I also have the means to treat Ich, Velvet, Saprolegniasis (not sure what it is though), and Trichodiniasis (not sure what that is either).
Future plans—Since I cleaned the hospital tank and performed a complete water change today, I will be testing the water parameters in the morning. I understand the nitrogen cycle and will be monitoring the levels for any necessary action. I’m willing to purchase any necessary medications to give this girl her best chance of survival and appreciate any help provided. Our local pet store only feeds one type of food (pellets) to the bettas but I feed a variety (flakes and freeze dried krill, pellets, and freeze dried bloodworms) to my bettas so I will be varying her diet as well. I alternate food types and only feed a small amount once daily.

 

[SaraB]

First get her into something bigger (like 2.5 gallons or up) with a filter.
Is she a crown tail or are her fins frayed? If her fins are frayed it could be fin rot and clean water could be the best thing for now.
It's hard to tell what the spont on her back is. Maybe a bacterial infection or missing scales? Does it look fuzzy like a fungal infection?
I'm noticing that she looks a bit bloated in the picture too
Is that just from her eating in the store?

 

[victoriamz17]

First get her into something bigger (like 2.5 gallons or up) with a filter.
Is she a crown tail or are her fins frayed? If her fins are frayed it could be fin rot and clean water could be the best thing for now.
It's hard to tell what the spont on her back is. Maybe a bacterial infection or missing scales? Does it look fuzzy like a fungal infection?
I'm noticing that she looks a bit bloated in the picture too
Is that just from her eating in the store?

I plan on upgrading her tank once she’s healthy. She’s simply in my hospital tank right now. I do frequent water changes as necessary and she has air flow. I’m concerned about identifying her disease to improve her condition. She’s not bloated, only appears to be in the photos. The growth doesn’t appear to be moldy or cottony. I’m not sure what it is. Her fins aren’t flayed. She’s a crowntail betta. My apologies for not putting that in the original post.