Welcome in H.C.M.
I have gone through your query and consider the medical history of sinusitis
and recently gb surgery.
As you throat is very sore and sufficient quantity of sputum is still there on expectoration ,so now it will be advisable to take some conservative steps for this also. In this connection I would like to suggest you for these investigations-
1- C.T.Scan of paranasal sinuses
2- Culture and sensitivity of throat swab.
3- Sputum for AFB & Gram's staining.
By this much work one may find out the pathological nature of infection and accordingly with the consent of your treating doctor this can also be treated.