So...we have: Mouth fungus, Dropsy, and Swim Bladder issues?
Here's some hope and wishes that he gets through all of this. I agree that you need to treat that fungus first. But some things to think about:
Why are you moving the shrimp to the hospital tank? I honestly think you should be treating the betta there since he's the sick one. I'd also consider doing multiple high volume water changes in the main tank in case there're spores or something infectious in the water. Plants do absorb medications, oftentimes with negative repercussions.
If the fungus ends up getting too thick, do consider trying to cut off as much as possible with tiny scissors. You can also use a qtip to wipe some off as well. Look up fish sedation with clove oil so you can operate quickly outside of the water.
I do agree that a deshelled pea is good for swim bladder issues, but bettas are carnivores, so I wouldn't be surprised about him not eating one; daphnia make a better source of fiber for carnivores IMO. However, I do not think he has swim bladder issues. If he's constantly trying to float to the top and sinking, or floating to the top and unsuccessfully swimming downward, he's got swim bladder issues. But by the way you describe it, he's just...being a betta.
Is that a missing scale that I see? Or is it simply miscolored?
What are your parameters (temp, pH, nitrogen cycle)?
Try not to be too hypochondriac with the betta. You're concerned, and I get that, but giving him a webmd's diagnosis is also harmful. Oftentimes, water changes and temperature changes can get a fish back from the grave, simply by better water quality.
Finally: as a preventative, try finding some Talisay/Catappa/Indian Almond leaves: they'll stain your water, but I swear that they're some of the best preventatives for soft water fish. They've got anti-bacterial properties, and help lower your pH; in conjunction with anti-fungal dried banana leaves, you've got a pretty good preventative for next time.
So many fish/plants/inverts to keep, not enough aquaria.