There is absolutely no data on how well homeopathy works for anything. That's not to say there isn't any research on homeopathy, there is in other countries, especially lately France, but anything that lacks patentability has very little money for the kind of research that would determine in double blind studies how well any natural remedy. Quite frankly, the data on medication is quite deficient, using very small samples and very short term experiments. Most medication has, at best, a 30% success rate, as measured by the few studies on depression funded by NIH. It's tough when profit is the motivation and source of the funding. Not much profit in homeopathy. But it's unlikely any homeopathic remedy would interfere with any medication, since there are no active ingredients in homeopathy. Now, amino acids, nutrients, and herbs can interfere with medication, at least theoretically, since they often target the same neurotransmitters. For example, many herbal relaxants target GABA, the same thing targeted by benzos, so it can be a theoretical problem. The same with serotonin targeting medications if you want to take 5htp or St. John's Wort, and of course MAOs interact badly with all kinds of things. The best thing for homeopathy, the only thing, is to see a homeopathic physician. Most homeopaths are trained as physicians, so they have some understanding of medication. If you see a naturopath, they should know of these contraindications, but again, it depends on who you see and how good they are. And doctors are downright ignorant and hostile to natural medicine, so they have no interest in these problems, for the most part. But if you google any remedy you're considering, you should find a site that includes the theoretical contraindications. Again, best of luck in your search. Also, I should add that much of the natural treatment of fibromyalgia isn't remedy based, it's more nutrition and exercise and lifestyle based. They use elimination diets and such to try to elevate energy as much as possible, keep the liver clean, which you can't do as long as you're on medication, keep the colon clean, and keep the body as uninflamed as possible. I managed health food stores for 18 years, and my customers with fibromyalgia who did the best usually did it with nutrition more than remedies, so perhaps a visit to a holistic nutritionist might be useful.
I think you might benefit some by looking at hormonal disfunctions with both BiPolar and Fibro symptoms. The thyroid really controls alot of thos symptoms.
Without homeopathy I'd probably be bed ridden. I've had fibromyalgia since 1992. In the early years when I was first diagnosed I trusted only in the traditional medical docs. Each one was doing what they do, practicing medicine not knowing what the heck to do with me. I can give you a list of about 40 different medications I've taken. With side effects so severe I plan to write a book some day. It wasn't until I realized this was my dis-ease and I needed to take a pro-active approach and be my own advocate. I started to realize how foods were making my pain worse and how my immune system was so affected by stress, by extreme temperatures, by lighting, by noise, by different smells. Things that traditional medicine could never help me with. Things that traditional doctors would never even ask me about. I met a great doctor a few years ago, he believed very much in the thyroid so I do agree with the previous comment, a low dose thyroid medication even if your blood work comes back normal will help dramatically with your pain and fm symptoms. I've been on it for years.
But the other critical part is the immune system. I take a chines herb, Astragalus. It's been used for centuries in Chinese medicine. Another great one is Grapefruit Seed Extract, I take that the moment I start to feel a cold coming on. I've just added iodine supplements and of course Vitamin D3000.
With bi-polar you do have to be extremely careful with herbs. There are herbs that stimulate the nervous system and that can interfere with bi-polar. It can cause manic events. There are other herbs that depress the nervous system and can cause the lows and depressive events so be very cautious and research "interaction" prior to taking something. The other key factor is foods. So many foods can affect depressive moods, pain and over all how we feel. High sugar goods, simple sugars like cakes, breads, soda can cause pain and depression. So make sure to include that in what you do. It can actually help you avoid taking so much medication. Another good medication for fibromyalgia which is an anti-depressant if you can take it is Cymbalta. It helps with pain and is often prescribed for FM.
I hope this helps a little. Best of luck. Bottom line its an over all approach, food, herbs, vitamins, medication, exercise. And therapy if you need it. Best of luck.