Yes you are correct . You are having Pyorrhea .
There can be many reasons for having sensitivity but in your case it would be due to your reducing gum line .
As there is deposits between your teeth and gum , it has to be removed. Oral prophylaxis is required in your case that is scaling , followed by polishing.
Next Steps
Consult your nearest Dentist
Health Tips
Avoid brushing with hard bristle brush, use brush with soft bristles.
Do not put excessive pressure on your teeth while brushing.
Brush your teeth twice a day along with mouthwash.
Ask your Dentist about the brushing techniques as he will make you understand better with models and materials.