What exactly are the water parameters? If it seems to have trouble breathing while salt appears to have rectify the issue, you may have elevated levels of ammonia and nitrite. Please state brand of test kit used. The aquarium salt itself is often used to neutralize the toxic effects of nitrite.
What do you feed your fish? Blood parrots, like goldfish, have greatly compressed GI tract so it is not surprising your fish is suffering buoyancy issues. What do you feed your fish? Please state brands used, ingredients ad guaranteed analysis. If your food products contain mostly starch-based ingredients, then these need to be thrown aside as starch is also one of the culprits for buoyancy issues. When the bacteria in their digestive system start digesting the starch, they also produce gas which when trapped inside the GI tract, becomes responsible for buoyancy issues. Switch its diet to veggies and gel food recipes. You could incorporate floating foods into gel foods to avoid "floaty" issues. You will find goldfish enthusiasts do that as several strains of goldfish unfortunately share this perennial problem. I also use gel foods for my goldies to avoid this issue. Blood parrots are no stranger to such issue.