Being a vegetarian has nothing to do with lack of protein or weakness as long you consume a balanced diet. In cases of deficiency you might expect more full body symptoms rather than just one arm.  However it still cannot be ruled out.  Every person born is genetically predisposed to a particular body type.  If you want to build your upper body strength you could join a fitness centre under the guidance of a good trainer. Kindly visit a physiotherapist who can guide you through this process and give you a thorough check up-to ascertain the cause of this problem.  If however you feel that is weakness/shaking has suddenly arisen then you should visit a doctor to know the cause.