I had a crown put in my back , lower,left side of my mouth. It started to hurt after a couple days, very badly. Went back to the dentist he said that it was the bite; drilled, threw cold water on it, and the pain was unbearable. Went to ER with infection on the mouth that night; it was prescribed Penicillin 500mg. After 5 days there is still sensitivity on it. What happened? Obs. Dentist never gave me antibiotics.
If your dental crown is sensitive to cold or heat temperature, you might be needing a root canal treatment, specially if the bite was adjusted couple of times. Your best bet is to see an Endodontist ( dentist who specialize in root canal) as soon as possible. We usually do not prescribe antibiotics for pain, unless there is clear infection, from the way you described your temperature sensitivity, it is most likely you have nerve inflammation, in which you must see the specialist dentist as soon as possible. In order to do the root canal, a hole must be drilled through the crown to get to the nerve, after completion of the root canal, depending on your cosmetic needs, you can either bond the top of the hole with tooth colored material, or if you do not like the patch work, unfortunately get a new crown.
Best of luck.