Alex definitely seems to have a bit more color in this picture. I can see the black spots that you're talking about on her dorsal fin, and I think that might just be the coloring. I know that all of my blue bettas have had those spots in their fins, and my black and copper betta, Amaro has them as well. So long as they're not rotting away and they're not raised off the fin, I think it's safe to say it's the coloring.
It's great that Alex's pectoral fins are growing in! That's a good sign, if I ever saw one. :)
You can hold off on the salt bath for a couple of days, I think that's probably a good idea. If it persists, though after a couple days, I would try one or two baths.
How is Alex swimming today? Any better than she has been?