You get exp in medicine each time a unit is killed/wounded, and each time a wounded unit is back at full health (+ your own hp regen) being in a settlement is just a faster heal, to level up medicine you need to cycle your units, recruit mass T1-T2, auto battle big army, have a lot of casualty, mass recruit, repeat.
Edit you don't actually need low tier unit, since higher tier have a better chance to survive instead of being killed, you get more XP since they will be wounded+healed, but massive army of recruits tend to have more casualties for the same battle