Grabbing the first aid skill should grant you access to two things
1.) A medical journal, a one-slot object that can be right-clicked to open up a "book" of sorts that tells you what cures what. Available entries depend on player discoveries, IE -- no entry for cold compress until you've discovered snow, wool, string. Maybe entries can be revealed when you've discovered more than half of the reagents, with the remaining reagents left as "???" slots. Crafted from Parchment, leather, any feather, black pigment.
2.) A tooltip on each wound that tells you what cures what if you've cured it before, or if you've discovered and crafted the cure. Only if you have the first aid skill, and only if you're carrying your medical journal.
I shouldn't have to go to an external wiki to look up cures for wounds, and I shouldn't have to mouse over various medicines to see what cures what. I think that's backwards.
The workflow goes like this: Player discovers they're wounded -> Player wants to cure wound -> Player gathers reagents -> Player crafts medicine -> Player cures wound
So why is the cure information on the medicine if the medicine doesn't come first in the workflow? The information should be given at the beginning of the workflow IE -- when the player discovers they have a wound.
It makes sense to hide this information from players who aren't trained in first aid -- but if I've purchased that skill, I should have ready access to medical information so I can USE THE SKILL.