Paradise fish wounds not healing

Question
Hi Lauren,

I have two male paradise fish in a 12L tank with a glass barrier between them (it is not sealed). I don't have a filter because my local aquarium advised that it was not necessary for Paradise fish and that for two fish, simply changing the water is sufficient. A few months ago one of them came up with a wound on top of his crown just above his eye. It started out small and some of the scales fell off but there has been no sign of infection. I have been using Melafix, white-salt and changing 50% of the water every 2-3 days. Unfortunately I haven't been able to figure out how he hurt himself until recently when my other fish had come up with a similar wound (and subsequent loss of scales) on his back between his dorsal and caudal fins. The fish with the bump on his head also has quite a large wound around one of his ventral fins and he has lost control of movement in that fin and the fish with the wound on his tail is also missing some scales on one side. I figured out (after much confusion keeping the tank ornaments away from them) that they were hurting themselves jumping at the glass lid of the tank and hitting the glass on the square edge where the lids divide to accommodate the barrier in their tank. It was not sharp but I have replaced it with a mesh lid and they haven't hurt themselves again since.

My main question is how long it will take for these wounds to heal up? The bump on the head has been there for well over 2 months now (and it has gotten bigger) and the other wounds have been there almost that long, with little sign of improvement (I sometimes think they are getting deeper even though there is no bleeding). The wound above the eye is most worrying because it is a few millimetres deep and causes my fish to twitch occasionally because of the drag - he thinks there is something on his head. If the wound around the base of his ventral fin doesn't get better I am worried it will simply just fall off.

There are no signs of infection, no white, black, red or fuzzy spots and I have checked the tank ornaments and gravel and they don't hurt themselves on those. I have lowered the water level to stop them being able to jump too high. They are relatively young fish, I have had them for about 4 months and they are only 1.5inches long (without their tails). This has been very baffling to me because their tails and fins continue to grow, their colours become more vibrant yet they still have these wounds. Aside from the twitching for the fish with the hole (it really does look like a hole now) in his head, their behaviour is the same as when I brought them home. They still fight all the time (through the glass! I'm not cruel, haha) and they eat plenty of food. I do very much enjoy having them as pets but I have tried everything recommended by my local aquarium and I don't want to lose them.

What should I do?

Answer
HOLE IN THE HEAD  
Symptoms: Holes in the Head, Duh
Small sores on head
Sores Spread


Symptoms of Stress & Disease

Hole in the Head General Description
This is pretty rare. Hole in the Head is a disease of tropical fish. Hole in the Head is most often seen in large Cichlids or other large fish. Oscars are large Cichlids and are often infected with Hole in the Head.  
Hole in the Head Treatments
The 'hole in the head disease' can be fatal and at present, very little literature is written about the cure for it. The symptoms that started off as a small "pimple" on the head erupts and grow into a deep crater that may affect the skull/head. Worst scenario is fatality and in lucky circumstances, it may just remain as scars on the face. Unfortunately, the disease is difficult to cure as it rarely responds to any medication. There are some water proof cream with antibiotic functions that can be applied to the injury areas but there's no real guarantee it will work.

There is one option. The combination of Flagyl (metronidazoel) and Chloramphenicol (Chloromycetin) usually does work to cure Hole in the Head. But these are both pharmaceutical drugs that require a prescription to obtain.  
Hole in the Head Prevention
You can help to improve the rate of survival by keeping the tank water clean with regular fresh water changes or using biological filters. The disease were said to be a cause from poor water quality with secondary bacterial/viral infections.

Hole in the Head often occurs in aquariums with under gravel filters, and sometimes in aquariums with canister filters, but rarely in aquariums with a BIO-Wheel filters.