It is normal to feel slight sensitivity and discomfort after the scaling , the severity also depends on the amount of deposits you had. The gums and teeth will take some time to recover. You can use an anti- sensitive toothpaste , apply on the teeth that are sensitive and leave it for 10 mins. Also can start with Vit C to ensure that the gums are healing faster around the teeth.
Next Steps
Ensure maintaining oral hygiene
Health Tips
Incase it increases alot do visit the dentist again.