and now you have peace of mind that your child did not have something more serious...
I never understood why people get upset when doctors will not just call in a prescription based on symptoms over the phone. Do you have a medical degree and have you invested the past decade or more of your life to learning about medical diseases? Doctors have. And every prescription they write is backed by their license and their career. If it turned out that your child had something worse that wasn't evaluated and had long term problems with their eye sight because of it, would you have said, "oh well, I guess I should've brought him in to be checked, it was my fault" or would your reaction have been "I can't believe that doctor didn't even see my child, prescribed the wrong medicine and now my child is suffering!"
Please remember that while most people go into medicine because they do want to help people, they are also investing a lot of time and money into this career that these days is seeing less and less reward. While it may be inconvenient and expensive for you to go for an office visit, just think of how it would be for the doctor if they lost their license and could never practice medicine again.
disclosure: I work in the medical field