I have a strange obsession with water, so I drink 3-5 gallons a day
That is an extraordinary amount of water for one person to drink in a day. You should see a doctor and get a chemistry panel and urinalysis done to see if there is a medical reason linking your obsessive thirst and the shaking. If your GP finds nothing, s/he may want to refer you to an endocrinologist. Diabetes mellitus ("sugar" diabetes), kidney diseases, hyperadrenocorticism (Cushing's disease), diabetes insipidus, and other diseases should be evaluated with that much water intake. Although it seems counter-intuitive, with these and related diseases you can actually drink huge amounts of water and, because the kidneys are erroneously dumping more fluid that is appropriate, still be marginally dehydrated.