I once got a fish bone stuck in my throat. I went to A&E and they looked down my throat and said that although it felt like the bone was still there, it was in fact just a scratch left behind by the bone. Your tissue is so sensitive at the back of your throat. It sounds to me like your stomach may just be a psychological effect of you worrying.
Try and calm yourself down, it will eventually heal and go away. Vomiting will probably make it worse as the stomach acid will irritate the scratch/wound.
Good luck