I doubt it's still that.

I think her recent weeping must have had a lot to do with what she sensed from Rand. It would have made any Green despair and fear for the world and want to weep, especially with the residual effects of losing her warder on top of that (also, Alanna must know she'll have to go through that once more soon..).

Then, there's the likely content of Verin's letter. Verin very likely told her that on the Eve of TG, the time to pay for bonding Rand has come. Alanna wanted to do the right thing, to her thinking, by bonding the Dragon, but she had to be told she might doom the world with this if she isn't cautious. The Shadow is all around Rand and knows of Alanna's bond, Verin knew this for certain. Alanna is facing a series of detestable choices, to undo the danger to Rand she's made herself: she can relesase his bond, she might pass it secretely to another sister chosen by Verin, or she can renounce her role as a Green and sit out TG, safely in hiding, because she can't put herself at risk of being killed or captured by the Shadow, as her death could be Rand's ruin.

Getting that sort of letter would easily explain Alanna's weeping. The potentially devasting consequences of bonding Rand put right in her face. If Verin told her the BA had known the instant she bonded Rand and she's been a risk for months now... that would only make it worse.