So disappointed with the follow-up! I call to make...

So disappointed with the follow-up! I call to make an appointment for my son who is already being followed at their home.
I explain that we saw an allergist following the consultation at the ophthalmic hospital and that the diagnosis is wrong, that we must see the doctor again to set up another treatment. There I am offered an appointment in 3 months! No, seriously! We are talking about a child who needs an appointment in the days to come and not in 3 months !! And NO, I'm not going to take him to the emergency room because he needs proper follow-up and not treatment to calm the inflammation!
I do not understand that proper follow-up is not offered in such a hospital.
I am torn between worry, fear and anger.