Hi all - sorry for the delay in responding to the questions - I was busy following up on a lot of the advice.
Just re: the moving her 300 miles - that was about 2.5 years ago. She thrived well and then went downhill in the last few weeks. The test strips I had weren't very good but suggested nitrate between 100 and 200ppm but also suggested my tap water was 100ppm which may be why water changes weren't helping.
Anyway the upshot is she is better now. I have no idea if I did the right thing or just got very lucky but here's what I did in case someone ends up searching for 'red pest' later on.
Firstly, we thought she had cut herself because she had a red sore on her side that was quite small. We removed a potentially sharp object from her tank. Then her tails got streaked red and red sores multiplied - within a day her entire underbelly was one huge red sore. It was very distressing to see and on reading up on red pest which seemed to fit, very upsetting to realise we were probably the cause for letting the nitrates build up in her tank and not realise it. We thought we were cleaning her tank enough but in retrospect we don't think the gravel suction was efficiently removing uneaten food/waste from the gravel because it was going through a hose to a bathtub the other side of the flat so just not enough suction probably. And also the water quality seems to have gone downhill considerably - the test strips suggest 100ppm but I appreciate they aren't accurate - I have a new test kit arriving tomorrow.
We tried melafix in her tank first but because the water quality was still so low it made no difference and she continued to get worse. That's when I came on here having bought the new smaller tank so we could completely clean the other one and if needs be run a completely new cycle with the fish in it once it had new gravel etc. Meanwhile, once in the smaller tank which had the recommended dosage of API aquarium salt in it, I also added the recommended dosage of Methylene Blue. And that was the last I saw of Flappy the fish really for about three and a bit days as unless she was right next to the tank edge, I couldn't see her. I only fed her live food - brine shrimp was best as they floated past her. Blood worms didn't get eaten because she couldn't smell anything in the antiseptic so they just hid in a corner and she couldn't see them in the blue.
The other thing I did... which was potentially dangerous... was I filled that small tank with mineral water (treated with my usual water conditioner) rather than use part of the aquarium water she was used to or even just tap water. At the time, I did it because I was concerned about getting her into an environment with no nitrates and what I perceived was much better quality water but I have later discovered that this could have caused real problems going from such high levels of nitrates to low levels of nitrates and can cause osmotic? shock. So don't necessarily follow my lead on that.
The old tank was completely emptied, the gravel and plastic plants thrown out, the filter and moss balls put in saved aquarium water, a couple of ornaments cleaned. I cleaned the whole tank thoroughly, washed the new gravel, filled up the tank with mineral water again so it wouldn't have nitrates in it (I can't use Purigen whilst I'm treating her but I have some ready to go), added some FilterAid from King Fisher in case there was any healthy bacteria loss and then ran it for a few hours. By this time, Flappy was sat at the bottom of the 'hospital tank' not moving about much which made me think it was time to move her as I was concerned about the rubbish filter in that tank etc so I made sure the waters were both the same temperature and then I guided her into the net and moved her back.
Unfortunately, she must have gulped a lot of air when I scooped her up and when I put her in the other tank she didn't move a lot and when she did, she sank straight down again. A clear sign of swim bladder disorder. Her sores were almost completely gone however and her fins were less bloodstreaked. She kept trying to swim for the next hour or so but it was clear she couldn't stay afloat and would come down with a bump. However, online it said this should pass and to not feed her until she was better. An hour later, she was already swimming a bit longer before she'd bump down and by the following morning (today), she was swimming about normally and perfectly able to stay afloat.
I am continuing to treat her with melafix but she seems almost back to her old self apart from slightly streaky fins. She certainly is doing well for a fan-tail who we believe is at least 8.
As I said at the start, I don't know if I did the right thing, or just got really really lucky but thankfully she pulled through. Now I need to work out what to do about the mineral water situation as I'm guessing it may not be the right hardness/pH for her? I do have purigen so I could go down the tap water once I finish the course of melafix but I'm also not sure if I just shouldn't keep with this seeing as she seems to be thriving?
I'll try to add pics to a reply if I can get onto the forum from my phone.