Field Medicine
Starting at 3rd level you can use the bonus action granted by your Cunning Action to make Wisdom (Medicine) checks or use a healer’s kit.

Bedside Manner
Starting at 9th level, you can make a Wisdom (Medicine) check to remove one mental condition affecting an allied creature. The DC is equal to that of the effect being removed.

Triage
Starting at 13th level, when your allies are taking a short rest you spend your time treating their wounds. Any hit dice spent during this time are maximized, taking the highest possible value.

Patch Adams
17th level AoE cleanse mental effects

I've been working on this idea for a while, trying to create an effective healer without magic. My nurse friend suggested the Patch Adams capstone, but I'm not too keen on it. Not every medic is a goofball, so having a feature tied to a personality type is too restrictive in my opinion. I'm trying to think of something that speaks to a highly experienced and skilled medic, like a Dean of Medicine. Not sure how to accomplish that. Thoughts?