hello and welcome to HCM,
You are very right in always considering and being careful when you are taking any medication especially since you already had a reaction to a previous medication.
However you must also remember that antibiotics are life saving drugs and in cases where they are required they must be given albeit after proper consideration.
Regarding the role of antibiotics in sinusitis, antibiotics may not permanently cure the chronic or recurrent sinusitis
but they are definitely indicated in the control and cure of acute bacterial sinusitis and may be even life saving in many situations. They also can prevent and treat the many life threatening complications of sinusitis.
So if you are feeling better then fine otherwise it is wise to take the prescribed antibiotic and am sure you will definitely feel better.
Dr Sriram Nathan