Paper is a good temporary fix if your gums are hurting really bad from forming an embouchure. However, my favorite fix to this problem is a product called EZO and you can get it from just about any drug store. You'll find in the denture section.
EZO is pink piece of wax that comes in the shape of a horseshoe. What I recommend doing is cutting it down into one inch pieces and storing it in a ziploc bag for your convenience.
What you do with the EZO pieces is to take one piece and put over your bottom teeth and mold it and until it fits comfortably like a glove. Then you form your embouchure like normal, only this time your teeth will not be penetrating directly into your gums, instead the EZO will act as a buffer.
You will be able to practice for a much longer period of time and your director will thank you