A 2 gallon needs to be cleaned 2-3 times a week, especially with shrimp. Contrary to belief, anything that cleans makes MORE waste than most people realize - plecos, algae eaters, snails and shrimp. Shrimp do not help keep it clean... They might eat algae but NO bottom feeder eats poop.
Cause of popeye: ammonia poisoning. Lower temperatures also makes the betta more prone to infections and parasites. Most common: columnaris, velvet, ick, popeye.
If you move him to a smaller tank you'll need to clean the tank every day in order to help him heal.