Soreness in the arms after a workout does not necessarily mean that you have gained more muscle. Soreness is often a result of lactic acid buildup in the muscles, which can happen when muscles are worked in a way that they are not accustomed to. While soreness can be an indicator that you have effectively worked your muscles, it is not the only measure of muscle growth. Consistent resistance training, proper nutrition, and adequate rest are essential factors in building muscle mass. So, while sore arms may indicate that you have worked your muscles, it does not guarantee that you have gained more muscle.
