Seems like either you have a decay in any tooth or there is gum recession leading to root exposure. If there is a cavity/decay it can be restored as you have only sensitivity to cold. Or if you have root exposure you may need desensitizing agents and periodontal procedures.
Next Steps
see a dentist nearby as soon as possible to get the needful done.
Health Tips
brushing twice daily with proper brushing technique and rinsing frequently.