In your case, under bite or deep bite not necessary to extract teeth. It will be depends upon your case, sometimes only alignment by jaw expansion, or supra eruption of your posterior or others method will be cured your deep bite. In your age may be skeletal correction would be possible. If required than some times orthognathic surgery will be helpful in your facial appearance.
Next Steps
consult with orthodontist and oral and maxillofacial surgeon for profile analysis and treatment plan.