each other at the same time.

B-Sand confirmed that the channelling sickness was not caused by the balefire incident in Shadar Logoth.
I can't find the source atm, however.

He also said that Samitsu was wrong when she said the wounds were contained.


I seem to recall that he experienced symptoms while channelling there in LoC (when Liah went missing). I don't have the books at hand right now, so I'll have to do a re-read to make certain, but in light of what B-Sand said, it seems more and more likely. Remember that there's only a few days difference between the Dagger Wound and the Balefire Crossing, and that during these days Rand was unconscious anyway.