Thanks for your question on HCM.
I can understand your situation and problem.
No, whitish thing is not your vocal cord. So no need to worry about it.
This thing is sputum (expectoration).
And your history and description suggest possibility of post viral
bronchitis.
So better to
consult pulmonologist and get done
1. Clinical examination of respiratory system.
2. PFT (Pulmonary Function Test).
PFT is needed to rule out bronchitis.
It will also tell you about severity of the disease.
And treatment of bronchitis is based on severity only.
So get done PFT.
You may need inhaled bronchodilators and antihistamines drugs.
Don't worry, you will be alright.