Mike,
I've been waiting to see if someone has an answer for you. My guess is, that there is no remedy for this type of discomfort. It comes with the territory. It is also my guess that the discomfort that you are feeling is an indication that the BCG's are stimulating the response that it is supposed to stimulate. This mindset seems to make this mild torture a little more bearable. Unfortunately, after the 3rd treatment, the BCG ante goes way up.
I still hope you get a more positve answer to your question.
Your BCG friend,
Rosemary