Will the swelling go away from osteoarthritis in my finger joint?

What does the Doctor say?

If the joint is deformed, no, the swelling will not go away.

If you are like most of us, arthritis just gets worse over the years...
Of course if you have just one swollen finger and are still young, I might wonder if the diagnosis was correct.
There aren't too many things other than injury that could cause a finger to swell, unless you have something really unusual like a bone cyst.