I have a throbbing intermittent pain 3 weeks after having a crown prep done.

It is not uncommon to have sensitivity or pain while wearing the temporary crowns.  This most often disappears after the permanent restoration has been placed.  You may have discomfort because your bite is slightly off.  Your temporary might be slightly loose and "leaking", which allows some bacteria to "annoy" the underlying tooth.  All those things can easily be addressed.However, my advice is to have the tooth evaluated by an endodontist (root canal specialist) to see if your tooth has been compromised to the extent that the pain will get worse, or an abscess will ultimately develop.  If by chance, you do need a root canal, it is better that it be treated before the crown is placed.  If the pain does not go away, and you end up needing a root canal after the crown has been cemented, the endodontist will have to drill a hole through the crown.  Although that is commonly done, it is still better to have the root canal, if needed, done first.

There are several possibilities for the source of your discomfort.  1) It is not unusual to have some post op pain following a crown prep.  This usually resolves with the new crown2) The bite may be a bit off on the temporary crown which can cause the tooth to be sore.3) Occasionally a tooth that has been prepped for a crown needs a root canal treatment.  The reason a tooth is crowned is because it has been damaged.  This damage can lead to the need for a root canal treatmentDiscuss your concerns with your dentist before the crown is seated.  I'm sure they will help you get passed the pain.  Good luck.