I think she's probably in Arafel helping the defenses of her homeland. I'm assuming from the timeline that this is connected with the invasion. It makes sense since Verin tells Mat about the Caemlyn invasion, so maybe she tells Alanna about what's going on in the borderlands... Personally, I've never got the BA vibe from Alanna. She has a temper and her own motivations, not to mention she's a little emotionally unstable. But I think she's loyal to Rand, in her own way.