Yes you can give some support as a girlfriend that is some company so that he can feel he has friends who care. At your age there not much you can do as a girlfriend, apart from giving him comfort as a friend by being there when he need a person to talk to. This is because much is usually done by the parents as well as the boys family members.
Most people just want to be left alone to sleep when they are sick and im sure he has a family who may or may not welcome you while hes sick. Give him a couple if days and be there for him during recovery when he may be more receptive to company.