Is Microbial Culture Required In Case Of Persistent Sinus Infection?

I have a very sore throat related to sinus infection for the last 10 days, I was taking Z-pak for the first 5 days. there was no relieve of symptoms. I feel worse. I also was taking different antibiotics for the last two months, including penicilin and clindamycin HCL150( for a root canal) then amoxicilin 250 for night chills. How to convince my doctor to do the microbial culture? I also take Enbrel and Methotrexate for RA with the evception for the last two weks. ET