Hi Maria,
If you have private insurance, pediatrician Dr Bene at First Med (Szena ter, 15 min on 4 or 6 tram from Octogon) is very good.
Good luck,
Jessica
If still relevant, Dr. Csákányi Zsuzsa is a very good ear doctor.
She works on WED mornings in Heim Pal hospital and she has a private praxis near Nagyvárad Tér (8th district).
In the same private praxis there is another doctor:
He works also at Heim Pal hospital on THU mornings. I guess he is leading the nose-ear department in Heim Pal.
They are both very good doctors. I have no idea if any of them speak english though.