I think you are correct to doubt that you have CH. (I'm not a doctor.) Your symptoms hardly sound like CH at all, especially the absence of excruciating pain. The only other kinds of chronic headaches that I know of that are one-sided are chronic migraines and hemicrania continua, but you don't describe having some key symptoms of either of those, either.
In the short run, you might try some ginger, which helps with the persistent low-grade pain in CH and migraines. Here's some info: >>>A teaspoon of ginger simmered in a cup of water, sweetened to taste, is a pleasant way to hold off the shadows for a couple of hours. Ginger doesnt dissolve well, so simmer the powder or finely chopped ginger root for a while, and keep stirring while you drink. In hot weather, a very strong ginger ale or ginger beer can do the trick enjoyably. Look in health food stores or delis for brands such as Reeds Extra Ginger Brew, Ginger Peoples Ginger Beer, Natural Brew Outrageous Ginger Ale or Blenheim 1903 Hot Ginger Ale. The usual ginger ale used for mixers, such as Schwepps or Canada Dry, is not strong enough. A company called The Ginger People makes strong ginger candy in several varieties (www.gingerpeople.com)<<<.
Did your doctor prescribe anything? As I say, it doesn't sound like you have hemicrania continua, but the prescription drug indomethacin is a very effective treatment for it, so you could rule that out (or in) pretty quickly.