There are a few problems with your setup. If the fish is 3 years old and still physically fits in a 10 gallon tank, he is likely stunted. A 3 year old fish - even a fancy goldfish - should be at least 8 inches long and would look quite cramped in a 10 gallon. Stunting is a result of being kept in a tank much too small for too long, and it can trigger major health problems down the road. A 20 gallon tank is the absolute minimum recommended tank for a fancy goldfish.
However, there are a couple other issues that could be causing problems. You didn't mention your water parameters or type of filter, so I'm going to assume you don't check parameters because you don't have a test kit, and you have the standard hang-on-back type of filter, the kind with the cartridge. The product you keep adding, Cycle, should be unnecessary once the tank is properly cycled, and these kind of "bacteria in a bottle" products are almost always useless anyway. They don't work.
I suggest you read our sticky on cycling:
http://www.aquariacentral.com/forums/showthread.php?t=84598
Once you've been through it, you'll understand how difficult it is to maintain a cycle in a tank with the HOB type of filter. The best way to overcome this issue is to float the new cartridge in the tank or clamp it to the side of the tank for at least a week before you put it into the filter, to allow some transfer of bacteria from the old cartridge to the new. Otherwise, every time you change the filter, you are throwing out your entire colony of beneficial bacteria and starting a totally new cycle. That can make your parameters spike wildly and make your fish sick.
It sounds like you really care about your little fish, and that's the best place to start from. Don't feel bad about the mistakes you've made - they are quite common and if your only resource was the pet store or wal mart employees, there's no way you would know any better. The important part is that you care for your fish and you're eager to help him get better.
Unfortunately, lymphocystis is untreatable, as are tumors. Another possible diagnosis is fish pox. Lymphocystis and fish pox are both viral infections, with no known cure. It's impossible to know what causes tumors, perhaps something in the water, perhaps the fish was genetically inclined to develop tumors... similar to tumors in humans, no one really knows.
However, the good news is that none of these commonly develops to a degree where they harm the fish. They look a bit ugly, and you could take him into a vet to have the growth removed, but he may live a long, happy life even with the bump. As long as his behavior doesn't change, he stays hungry and active, there's nothing to worry about.
I do recommend that you buy a larger tank soon, though. As soon as possible. There are often 20 gallon tanks in our classifieds section - you might even post a wanted ad in the classifieds if you can't find one. A 30 gallon tank would be even better.
If you have the opportunity to buy a better filter, take it! If not, you can maintain your cycle as I said, by keeping the new cartridge in the tank water for a week before you put it in the filter. Throw away the Cycle, and cut back on the salt in the water. Salt is a good treatment for some diseases, but there's no reason for using it all the time. And buy a test kit! The liquid kits are the best - they're expensive, but they last quite a while and they are definitely worth it. Then you can keep track of all the chemicals in the water and keep your fish as healthy as possible.
Best of luck, and keep us updated on your little fish.