Hey there. Welcome aboard the forums.
One of the already planned goals for Adventure Mode is to have every available skill from Fortress Mode at your disposal. That encompasses medic skills as well.
Also, it has been already asked and implied at the Future of the Fortress megathread that dwarven medics at NPC fortresses should be able to heal you.
If those long-standing goals are just too far away from you, here I can help you with an array of solutions, so you can choose what suits you best with the current 0.34.11:
Enter Fast Travel, move a single square and then return to adventure
Pros: works with bleeding, open wounds (before they get infected), cuts and bruises. Also heals your damaged companions, if they're with you when entering Fast Travel. May leave badass scars.
Cons: Doesn't work inside bandit camps, near rivers or inside buildings. Cannot heal damaged arteries and nerves.
Retire your adventurer
Pros: almost any kind of damage is healed.
Cons: Must be done inside a hamlet, town or stronghold. You may lose your companions. Lost limbs are not healed.
Turn into a werebeast
Pros: Completely heals you for every full moon month that comes by, including lost limbs and nerve damage. You turn into a savage death dealer while that happens.
Cons: Getting bit by a werebeast is a dangerous task on itself. The most awesome werebeasts (mammoths, bulls, lions) will rip your guts out of your chest with a single kick before you can even say hi. Vampirism becomes impossible at this point.
Turn into an undead thrall
Pros: become feared by everyone, be virtually invincible, pain isn't even a thought anymore.
Cons: become feared by everyone, good luck finding a thralling cloud and surviving long enough to breath from it. Vampirism, necromancy and lycantropy become impossible at this point.
Hope it helps (: