You must know that not all sinuses
are fully developed in a 6 month old. Only 2 main sinuses, ie ethmoid and maxillary are present and these too are very small. Moreover sinusitis
itself is not very common in this age group.
If she has had rash on and off since her birth, you must keep the possibility of atopic dermatitis
in mind. Usually there is a maternal history of asthma
or dermatitis. The problem is quite severe early in life but many children "grow out" of the problem by 5 or 6 years of life.
If the condition has worsened after amoxicillin
, it should be discontinued with immediate effect.
It could be a drug reaction.
Your child needs to be shown to a Skin specialist for the correct diagnosis and management.