You say crown at first then mention cap. Which is it? If crown (tooth on post) it should be dead after root canal, but if a cap (veneer) this will go over the old tooth after being filed down and, yes, this could be painful as it is exposed, and will need revisit to the dentist.
You have my sympathy as I am going through similar at the moment, with broken veneer at the top and needing a crown below it on the bottom. The temporary veneer lasted just under 2 days.