Metallic file was broke inside tooth during root canal. tooth is hurting and keeps infected. what are the prognoses and implication. ?

It depends: Depends upon how deep into the root the file is lodged; was the canal disinfected with medication and smaller files before the separation; can the file be removed or bypassed... Generally a broken file has the highest success when treated by an endodontist (advanced training and equipment). Prognosis could be anywhere from poor to excellent.

See an endodontist: The a separated file does not mean that the tooth will fail. Removal of separated instrument from root canal is often a very difficult procedure, but an endodntist, an adequate technique with as small instruments as possible may be a key to success.