I don't have enough information to make a formal diagnosis, but from what you have described, it seems that you are having some tremors. Tremors are involuntary movements of the limbs or the head, which may occur at rest or with movement. There are different types of tremors: Rest Tremors and Postural Tremors. Rest tremors are the tremors seen in Parkinson's Disease; this type of tremor disappears with sleep and occurs when the patient is awake but inactive. Postural tremors include physiological tremors/essential tremors which are tremors that are absent at rest but occur during intentional activities (holding arms outstretched in front of the body, writing). These are the tremors that we see in anxiety, fatigue, toxic or metabolic abnormalities such as caffeinism and hyperthyroidism. It is also commonly seen in patients taking Lithium, antidepressants, and alcohol. About 10% of patients on Prozac complain of tremors as a side effect and you might want to discuss this with your physician.
I hope this information was helpful to you. It is however for general education purposes only and is not intended to be a substitute for professional advice.