Your baby seems to be having Erbs palsy which is due to tractional injury to the nerves in the arm. Most often it is transient and improves over a period of time. But now you should start some exercise to improvemuscle power and also to avoid formation of contractures you shall keep the arm in a proper position. This can be explained to you by Occupationaltherapist / Physiotherapist. If the arm is absolutely limp and there is no improvement over next 3 months we should investigate for further action.