Hello there, 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. Take care.