Your ginger candies might or might not be strong enough and gingery enough to give ginger a fair test. Strong tea is probably better, and you can add honey or other things to make it more candylike. Fresh ginger cut up and boiled is the best tea. Some people make it from powdered ginger, but that's a gloppy process.
Many/most docs are a lot more comfortable prescribing meds than prescribing O2. Lithium is a ridiculous initial suggestion. The literature is clear that lithium is not advisable except for patients who are chronic, in part because the side effects are so undesirable and in part because stopping lithium often leads to severe rebound attacks. Topamax is less ridiculous, but not a whole lot less. I would encourage you to try to find a competent (regarding CH) neuro, which you're most likely to encounter at a headache center. Or. if your current doc is amenable to your suggestions and willing to consider your input, you could stick with him/her, because if you stay at this site you'll know as much as s/he does about CH meds, and about all s/he is good for is prescribing things you can't get for yourself. If some of the possible pharma treatment breakthroughs occur (e.g., if Lilly's new drug, Emgality, lives up to some people's expectations), you'll need a doctor to prescribe them if you want them. By then, you might be very effectively managing your CH with mostly-non-pharma treatments.