My mom had an abscess tooth removed, but now her cheek and neck burn. what can she do?

Best to go back to the dentist/oral surgeon who extracted her abscessed tooth.  S/he can then look for traumatic injury to the nerves in the area.  Perhaps she's running low on some vitamin or mineral.  Early presentation for shingles (zoster)?  

There are some newer meds that deal w/burning & radicular pain.  Best to chat w/your family physician to consider a trial of one of these meds, eg gabapentin, lidocaine, duloxetine, etc.  Good luck!