Mysterious Lump along with Worms?

First, some parametersr!
5 gallon filtered
Kept at 75 degrees (though heater has broken and new one is coming, so been about 70 for past week).
0 Ammonia, nitrites, nitrates around 5-10 ppm
Only other fauna is an Amano shrimp.

So my betta Gordon has been suffering from some pretty bad fin rot and a weird bloat. At first I thought the bloat was because I was overfeeding, but his food rarely touches the bottom. He has skipped a day or more of food and nothing odd has happened, so I thought he was just getting fat (especially since I rediscovered some frozen brine shrimp in my feeder). Well the lump wasn't going away, but, not trying to take the blame away, I'm getting into finals mode and a supposedly chubby fish was the last thing on my mind with several huge projects due in such a short amount of time.

I started treating salt for fin rot, nothing was happening, and with a long weekend to spare in between work on final projects I decided to give him a salt bath and the weirdest thing started happening. I was observing him and he breathed heavily with his gills and a tiny worm, less than half a centimeter long, kind of pale ish popped out of his gills. I noticed there were a few others worms in the water and realised that that lump probably isn't just some fat.
I was reading around, however, and people with similar problems concluded it was a tumour and not a parasite of some sort. So could it be a tumour and Gordon has the bad luck of having really bad fin rot, a tumour, and worms in his gills? Or could they be related? How should I start treating (for internal parasites?). Thank you very much.
The pictures below are blurry, but you can sort of make out the lump by his face. It also shows up as pale/pinkish in some of the photos.