I am having jaw and full mouth pain and water sensitivity after having 20 crown veneers placed last month. What's the problem?

Early sensitivity after veneer cementation is not expected, but can happen.  This usually subsides within 4-6 weeks but can last longer.  Drink through a straw until then.  If it does not subside on its own your doctor can call you in a small steroid pack to help if needed.  Also, have him/her check your bite to make sure it is even.  A bite that is off can co tribute to tooth sensitivity.   

Sensitivity to cold is extremely common following veneer cementation.  The cement that is used often triggers a nerve response that will diminish with time.  I always inform patients that this will be the case.  If you drink something hot or cold and you feel sensitivity, it should go away immediately and not linger.  Also, it shouldn't hurt when there is no hot/cold substance in your mouth.  If it does, then you have nerve damage instead of just sensitivity, and the tooth may require a root canal.
Next and muscle pain is usually due to trauma from the procedure, i.e. having your mouth open for hours at a time.  Add in new veneers that change the biting surface, and you have the perfect storm.  Wear a night guard.  Sometimes muscle relaxers are necessary to calm down your muscles so that you can heal and your doctor can prescribe them.  A soft diet for three days should be attempted to again let your muscles relax.  There are also massage therapists that specialize in oral and neck massages that can help.  
If you attempt these things and the pain still persists, it is more than likely a tooth and you need to have your dentist revisit your xrays.