It might also be a piece of bone. It happens commonly. Even if it is a piece of tooth, don't worry. It can be removed. Just take an x ray. Visit same dentist. He/she will guide you and help you.

Hi...I would suggest you to go to same dentist immediately, as he would be right person to assess the wound..what u found,  can be part of bone(that surrounds tooth) or may be part of tooth...get it examined and treated...and get xray also done to make sure whole tooth is out...Don't wait for 10days...

If you are confident , and trust, please visit him.Get an X-Ray done.And get the remaining tooth extracted.. OR Consult another Dentist .After X-Ray and if necessary go in extraction. Sometimes the remaining tooth may need a  minor surgery to remove it. If there is pain and it is not subsiding with the present medicines, then get the medicines changed.This will depend on the severity of the infection and the need for a normal extraction or a surgical approach. As far as possible surgery should be avoided to maintain the integrity of the oral tissues.

This might be a bone fragment but its better to visit the dentist and get it confirmed with xray. Better to go now as you are already on medications