As per your history your daughter 4 year old is sufferring from conjunctivitis
for which she was on treatment with antibiotic eye drops. Hydrocortisone
is a steroid and it should be avoided in infective conditions. Steroids
are used only in cases of allergy
related conjunctivitis under supervision of an ophthalmologist because of the potential complications of steroids.
Eczema be seen in severe conjunctivitis or in cases of blepharoconjunctivitis or in cases of viral infections.
I advice you to consult near by eye doctor for correct daignosis and treatment.