I assume you have ADHD and Wellbutrin is used off-label (it i not FDA approved) for ADHD. It can be beneficial to some people alone or with other medications (Adderall and Wellbutrin for example). Wellbutin acts on dopamine, one of the neurotransmitters stimulants acts on. The vast majority of people with ADHD respond well to stimulants, only a few do well on Wellbutrin. Normally people who take stimulants and don't get better tend to have a good response to Wellbutrin or Strattera, an FDA approved non stimulant medication.
People on Wellbutrin commonly have twitches and movements like your hands. In some people they can have seizures. And if he is fine prescribing Wellbutrin even though you have a tremor and he won't do anything I would say that is improper.
What should you do? Get a new doctor. Doctors do have personal opinions and most have some self imposed policies (like not prescribing certain things). That is fine and it is appropriate for a dermatologist to decide never to prescribe Adderall because that would be VERY inappropriate. But a doctor treating ADHD (ideally you are going to a psychiatrist) really needs to be willing to prescribe the FDA approved treatments like Adderall. If he won't then move on. If doctors are not willing to prescribe multiple types of treatments then what is the point? Or his "not believing in it" could be a way of saying Adderall is addictive and there is no way in hell you are getting it.
Adderall might be great for you or it might not be. You need to see a doctor say what your symptoms are, answer their questions, and NOT say "I want Adderall" or "can I have Adderall." You might mention the medication but you need to let the doctors do their job and figure out a good treatment. So what you need is a doctor who will try multiple things and does "believe" in other treatments besides Wellbutrin.
I am a medical student at a university in Montréal, QC, Canada for psychiatry and internal medicine. I have a Hons. BSc in pharmacology and I have interned with two psychiatrists and one neurologist. In addition, I have worked as a pharmacy assistant.