Your child should be fine. Most likely your pediatrician placed you on either Zithromax, augmentin, or omnicef all of which cover pneumonia. As the previous poster said, pneumonia even in a healthy child will take 1-2 weeks to get better. As long as your child is staying hydrated, the fever is gradually coming down, and showing no signs of shortness of breath/air hunger (rib cage flaring in and out with breathing, increased breathing rate, nasal flaring, loud wheezing) they will be fine. It's absolutely the scariest thing ever when your little one is sick but watch for those symptoms and you will be set.

As far as seeing a specialist, pneumonia is unfortunately common even in young healthy kids so if you have any concerns would recommend followup with your pediatrician prior to seeking specialty care.