Constant cough in 4-1/2 years. Its own?

Dear Doctor: My daughter is 4-1/2 years and she has cough for the last 5 months..We have consulted three doctors and they gave some syrups and the syrups gave only intermittent relief, if we leave the syrups for 2 days again she begins to cough. We tried some conservative measures like boiled ginger water with honey and it is also worthless. We are confused and do not know what to do...Now, we are giving Dextromethorphan Hydrobromide, Chlorphenairamine maleate & Phenylephrine Hydrochloride Syrub. Our general doc told that she has some muscle growth on sides of her tonsils and advised us to give her a solution named Povidone-Iodine Germicide Gargle 10 mL to gargle. Is there any final solution? or will it be cured on its own?