Everyone has an Adam's apple; they're just more obvious in men.
It sounds very much like you've had an attack of "acute" thyroiditis - also known as "painful" thyroiditis. The thyroid is a butterfly-shaped gland that lies at the base of the neck just below the Adam's apple. My guess is reinforced by the fact that there seems to be some enlargement of the gland, based on your observation that it moves when you swallow, and the fact that you feel a "golf ball" sensation in your throat.
I don't believe there's much that can be done about it. It usually runs its course, with only aspirin as a pain reliever needed. It can take a few months, though. You can research it and return to the doctor to educate him if you want. Have him do a thyroid exam... something it doesn't sound like he did yet, probably because he hasn't learned the art of it.