There is no home remedy for an infected tooth. Once an infection sets in, it is necessary to see a dentist and get antibiotics. Home remedies are good for prevention and for treating minor ailments - not infection.
Good home remedy for infected tooth problem is to apply clove oil twice in the affected area. One should not drink cold water or have icecream , instead should take lukewarm water. Have salt water gargle in the morning and evening and best advise is to consult the dentist.