Can i sue the dr. who diagnosed my 3 year old son has pneumonia and prescribed antibiotic?

My son is 3 year old. Last week, he had severe cough and fever. So, I took him to the pediatrician. He was very difficult to breath. She prescribed oral steroids and told me to take him to St. clair hospital ER. So, I went to ER. There, the doctor checked him and took x-ray. After seeing the x-ray, she diagnosed, it was pneumonia and prescribed antibiotic. He took antibiotics 2 days. But, the condition is so worse. So, I took again to ped. Again they repeated the samething. He was findig difficult to breath, oxygen level is low. So, she arranged an ambulance and I took him to childrens hospital ER. In childrens hospital, again she took another x-ray and she diagonised that it was not pneumonia some virul, so,stop the antibiotic. So, can I sue the first dr.?. please advice me.