Most often cough and cough in children is caused due to certain viral infections and such infections do not generally need treatment with antibiotics. But since the antibiotic septran has been started, the course should be completed in order to avoid development of antibiotic resistance. Generally such episodes do not last for 3 weeks and you need to get the child evaluated by a pediatrician and he would also be able to look into the cause of the vomiting as well. I would insist you to take the child to a pediatrician for the same. Apart from clinical examination, he might need to run a few tests to be sure. Treatment would depend on his findings. Meanwhile you may give the other medicines but giving some antiallergic like cetirizine. Some steam inhalation should be helpful. Some anti-emetic might need to be given.