If i was your doctor i would recommend you to get your x ray soft tissue
neck done to rule out if there is any piece of bone left in your throat or not. If you are able to breath normally and you are able to eat and drink then most likely the bone piece is not there. The discomfort that you are feeling is because of the abrasion in your esophagus
that resulted while the bone was passing through it. It will heal with time. There is nothing to worry about. Also do glycerine gargles, it will help relieving the discomfort. Take semi solid and liquid diet
till it heals completely.