Welcome in H.C.M.
I have gone through your query regarding mucous producing chronic cough
and you have already taken antibiotics , steroids
but no relief is there.
No doubt you are having chronic respiratory tract
inflammation involving your throat and chest. Most likely you are having allergic bronchitis
but to made proper diagnosis and treatment you should do-
1- X-Ray chest.
2- Culture and sensitivity of throat swab.
3- Pulmonary function test.
4- Sputum for AFB.
Apart from this good clinical examination of cardio-respiratory system is necessary for plan for treatment.