The shaking feeling could very well be attributed to low blood sugar levels due to not eating enough. I get very shaky feeling if I do not eat enough. Prozac will not really make you eat its just supposed to help the depression. If the eating is directly related to your depression then as the depression lifts the eating should get better. If it doesn't than the eating could be a seperate issue. The questionable thing is the burning sensation which should definatly be brought up to you doctor.