I think you should write an addendum to explain (a) why you retook the test in the first place, and (b) why your score was so much higher the second time. It sounds like the poor environment of the testing center during your first LSAT was the reason for both.
My advice for the addendum is to keep it short. A couple of sentences, no more. Let the legitimate reasons for your improvement in score speak for themselves.
And don't say that you were sick if you weren't.