Even if BS doesn't want to confirm it yet:
Q: "It’s pretty clear now that Moridin and Rand are linked because of the balefire incident. Since Rand used saidin to create the balefire, and now he gets sick when channeling saidin, does that mean Moridin gets sick when he tries to use the True Power?"
A: "You’re assuming that Rand’s channeling sickness comes from crossing the streams."

The sickness it started shortly after the episode in SL, where Rand saw the first time doubled and became dizzy:
"Dimly he [Rand] was aware of another bar of pale solid fire rising from the other man's hand that was not clasping his, a bar slashing the opposite way from his. The two touched. Head ringing like a struck gong, Rand convulsed, saidin and the Void shattering. Everything was doubled in his eyes, the balconies, the chunks of stone lying about the floor."

I generally like your idea. It makes sense, because the dizziness just occurs, when Rand grasps the OP or lets it got (this fact speaks in my view against the idea that the SL wound is responsible). IMO, it doesn't really explain, though, why the sickness becomes worse.

Therefore I would suggest that the sickness has more to do with the fact that Rand and Moridin's threads in the Pattern were fused together by the balefire. IMO, the Pattern tries to correct this somehow. Since there seems to be an effect of the Pattern on you if you channel (e.g. Min sees more Images, if a person channels), maybe the Pattern/Wheel has more control over Rand's and Moridin's threads, when one of them channels, ie. is linked to the True Source. I believe the Pattern interweaves their threads more & more to basically correct the anomaly of two threads "physically" linked, so that in the end only one thread would remain again.

This might explain why Rand and Moridin become more and more similar and why the sickness becomes worse.