Yes I think I see the white something on the gill but I am not sure it's ich or just the photo or his colors (and it could be stress ich even if it is). If there aren't more white spots by now, it's probably not ich.
I did mean ParaCleanse - sorry about that!
If you want, you can do a med trio approach too (ParaCleanse, Maracyn, and Ich-X) where you treat for everything at once. That would cover all your bases for ich, bacterial fin rot, and parasites and it's the standard Aquarium Co-Op quarantine method too. But medication can be hard on your fish and medication will not fix stress-caused illness.
I think you can treat either the hospital tank or the main tank because ParaCleanse (as well as the med trio) is safe for plants, snails, etc. ParaCleanse will not stain your silicone but Ich-X might, so I would be careful of that. Since you have an otocinclus in there as well, it may be worthwhile to treat the other fish while you're treating already. Otos are wild caught so they often carry diseases like gill flukes. Gill flukes are also very contagious.
Re: stress, it is possible that moving your betta to a new environment like a hospital tank will stress him out, but it's also possible that moving him away from whatever is stressing him out in the main tank is going to help him get better (esp if his tankmates are the reason for his stress).
Personally, I am a bit cautious about medication (esp antibiotics) and I don't think his fin rot is that bad yet (i.e., not close to invading the body). So I would probably treat the entire main tank with two rounds of ParaCleanse (assuming your main tank isn't very large and it wouldn't cost too much to treat) a few weeks apart and do a wait and see approach on the fins. If his fins REALLY start getting worse at any point, I would put him in a hospital tank immediately and start treating with Maracyn or salt immediately. It has been my personal experience that betta fin rot responds really well to salt treatment, but salt is no good for plants and snails. But you know your fish the best and I also think pulling him out to a hospital tank now would be a reasonable approach too!
In any event, I would definitely also test your main and hospital tank water very often for the near future to see if there is anything going on. I noticed my tank when I first started would go through pH swings throughout the day because it was not as fully cycled as I thought and those pH swings caused my betta to get fin rot.
Also I should mention that in general bettas prefer temps slightly higher at ~78, although I highly doubt that your temp being 75 degrees is the main reason for everything that is happening as long as that 75 degree temp is stable.
Good luck! 🙂