You are Type I diabetes
and hope it is under control with the use of insulin, The symptoms and history which you have given indicates Post viral state where secondary infection and with the use of Proper antibiotics it should subside, It is prolonging as you requred salbutamol
it means bronchospasm
is there ,in such cases a nebulizer
therapy may help you . Also post viral dry cough
persist for long time in some cases. If your brochospasm is relieved may take antitussives in consultation of your chest Physician.
In any case if no relief go for X ray to rule out any significant pathology as you are a Diabetic patient.
Best of Luck