The problem with the gourami could be a number of different things. Before attempting to diagnose anything, we'll need to know those nitrate levels in teh tank.
How much decoration is in the tank? Can you give more details about symptoms?
As for the debate about algae eating animals... For starters, in a 20 gallon tank I would not put more than 3 - 4 ottos in there, if working with ottos. A BN would be safe, but will outgrow a 20 gallon tank. Shrimp would be ok, and the fish should NOT eat the shrimp. The tricky part with the shrimp is in getting the right species if you're wanting them to eat algae, as not all shrimp eat algae and some shrimp can eat fish.
We may find that when you check nitrate levels, if there is an elevated nitrate, it is part of what is causing an algae bloom, and if the water params get fixed, a lot of times algae will go away on its own. I would also suggest checking phosphate if it's a hair algae, and I'd want to know how old the light bulbs are and how long in a day they are kept on.