I'm not sure, really.  I'm inclined to allow first aid attempts until they fail, representing the discovery of a wound that could not be treated in the field.  The medical bay will be happy to supply your character with whatever quantities of Stimm, Spur, and Wideawake he desires to help him through his troubles, and there's also spending fate points to recover damage.  (if you do so and roll high enough to recover to lightly wounded, you'd heal 7 wounds in the scene with the xeno doctor)