Jenna,
Have you found the wax at the pharmacy or had someone get it for you?
Back when I was on the farm we always had parafin wax for when we bottled jam.... you could use something like that... or even some hard sugar free gum if the jagged edge is hurting you too much.
More likely than not you had a cracked tooth or a Wisdom Tooth with some decay in it... thus the shattering to pieces when it broke off.. (Don't worry, if you swallowed it.. it will all come out in the end...

) )
Perhaps you could have them call in a prescription of Valium or Ativan to take an hour or so prior to your arrival at the office. (Be certain to have someone drive you and bring you back)
See if they can give you nitrous oxide.... that almost always helps. I had a 20 year old drive all the way from Prescott to see me today about taking out her lower wisdom teeth. I remove them if they are easy, but if they are impacted or have curved roots, I refer them out to an oral surgeon. I took some x-rays and sent her to an oral surgeon that had some extra time this afternoon.
About six months ago I had a 19 year old young man come in to have his wisdom teeth removed. They looked very straight forward. I didn't even use nitrous on him. Start to finish they were all out in 15 minutes and he said he barely felt one of the 10 injections I gave him.
He went to work the next day and said he didn't have any discomfort.
SO, what I'm trying to tell you is, it's no big deal. Dentists pull so many teeth it just becomes very routine. Just relax, have some faith and know that we are all pulling for ya. (pun intended)
PM me if you have any more questions...
BTW.. there are two of us on here who are dentists.... chickygirl2 (Patty) is also a dentist who lives in Upper Marlboro, Md. (I had some ancestors who had land there in the 1700s)
Good luck and God bless.