Reading the PHB, it’s pretty clear that the Medicine skill does nothing to aid in the treatment of wounds, ailments, or diseases. As written, it only allows for stabilizing dying creatures and for diagnosing illnesses.
Here are my slight changes to Medicine (and associated changes to the healer’s kit and Healer feat):
Medicine. A Wisdom (Medicine) check lets you try to stabilize a dying companion, evaluate others wounds, diagnose illnesses, treat poisoned or diseased creatures, and examine corpses in order determine the cause of death.
With a successful Wisdom (Medicine) check you can stabilize a dying character at 0 hit points.
Medicine may also be used to provide long-term care to poisoned or diseased creatures. When a poisoned or diseased creature is cared for by someone proficient in the Medicine skill, they make their recuperation saving throws (see Downtime: Recuperating on page 187 of the Player’s Handbook) with advantage.
Healer’s Kit. This kit is a leather pouch containing bandages, salves, and splints. The kit has ten uses. As an action, you can expend one use of the kit to stabilize a creature that has 0 hit points, without needing to make a Wisdom (Medicine) check.
If you expend one use of a healer’s kit to treat a poisoned or diseased creature, they make their recuperation saving throw (see Downtime: Recuperating on page 187 of the Player’s Handbook) with advantage.
Healer. You are an able physician, allowing you to mend wounds quickly and get your allies back in the fight. You gain the following benefits:
- You have advantage on all Wisdom (Medicine) checks.
- When you use a healer’s kit to stabilize a dying creature, that creature also regains 1d6+4 hit points.
- As an action, you can spend one use of a healer’s kit to tend to a creature and restore 1d6 + 4 hit points to it, plus additional hit points equal to the creature’s maximum number of Hit Dice. The creature can’t regain hit points from this feat again until it finishes a short or long rest.
Recuperating. You can use downtime between adventures to recover from a debilitating injury, disease, or poison. After three days of downtime spent recuperating, you can make a DC 15 Constitution saving throw. If you are treated by someone proficient in the Medicine skills, you have advantage on this saving throw. On a successful save, you can choose one of the following results:
- End one effect on you that prevents you from regaining hit points.
- For the next 24 hours, gain advantage on saving throws against one disease or poison currently affecting you.