Teeth polishing or commonly known as scaling does not need any injection unless your gums are very sensitive and tenderness is present. Time taken will be around 15 -20 mins.
Rates vary from dentist to dentist and also on the severity of satins and calculus deposited. Generally the rates are between 700-1000 rs.
Next Steps
You can visit a dentist nearby your place and get scaling done.
Health Tips
Brush your teeth properly used a good toothbrush take required amount of paste( remember taking too much paste is not recommended it should be a pea size). Also rinse your mouth properly after every meal.