DO NOT remove the ring!
This could complicate the situation to dangerous extremes!
If a piercing is infected, the ring keeps the hole open and allows for the infection to drain. If that hole closes up the infection could become an abscess.
It is unlikely that it is the type of ring that is causing the problems. However, it is not impossible. Some folks have bad reactions to anything that is not hypoallergenic. Surgical steel is the best option for first-time piercings, but some people opt for cheaper rings and some piercers provide cheaper rings as starters.
Here's what you do: STOP applying cortisone cream. The cortisone itself will not hurt you, but the cream and the inactive ingredients it contains can exacerbate the infection, providing a warm, moist area for the bacteria to proliferate.
Keep the area clean and dry. Use a blow-dryer to get moisture out (low setting, of course). Follow with salt-water soaks four times daily. I forget the proportions needed -- do a web search and find out. It's a smallish amount of salt to a portion of warm water. You can pour the saline solution into a cup and hold it over the infected area for about fifteen minutes several times daily. Then dry the area. You can use whatever method you find easiest to keep the salt water on the piercing.
Do this for at least a week or two. You should notice improvement in a few days. The salt helps kill bacteria and stops them from reproducing. Even if you see improvement, continue with the soaks for at least a full week.
If this doesn't help or if you see that the infection keeps on returning -- you MUST see a doctor. Also, if the infection gets worse AS you doing the soaks (unlikely, though), you need to see a doc. Antibiotics may be required here if the salt water doesn't take care of the problem.
Just NEVER remove that ring -- and NEVER apply anything BUT salt water. You'll only make things worse if you don't follow these instructions.
If you notice any increase in swelling or redness or streaks radiating out from the area -- get medical attention AT ONCE as this indicates the infection has become very serious.
Many piercings go through an up and down phase during healing that can last up to six month or a year. Sometimes folks get repeated infections during this time, but many do not. Usually salt water soaks clear these up right away and there are no further complications.
However... two years is too long for this to keep happening. So give the salt water soaks one good try for up to two weeks. If the infection recurs or does not clear up -- you MUST see a doc to handle this.
Hope this helps!