Hi
You have two symptoms
Sweaty palms and cough
For sweaty palms if this is seen more when you are anxious then seems to be normal but even in normal conditions it is sweaty then you need to check your
thyroid hormone levels.
While for cough , persistent cough for long time needs evaluation in detail,you might require to do x-ray chest and sputum examination to rule out serious lung ailments.
So I would suggest you to visit an ENT SPECIALIST doctor and seek proper help
Regards