How healing works and how damage works are intrinsically tied. Before discussing either, we must first determine what we want the mechanics to represent.
I want characters who can be injured, and I want injuries to take a long time to heal, but I don't want characters getting injured in every combat.
I want a small amount of penalty to actions based on pain, fatigue, and injury, but I want it limited and easy to track. It should avoid the death spiral while still having a meaningful mechanical effect.
I want rage, inspiration, and fear for their children to temporarily grant characters the ability to fight well despite pain and injury, and to fight better when they're healthy.
I want divine magic (positive energy) , and only divine magic, to be able to quickly heal small cuts, burns, and bruises during combat. It should heal damage at a consistent rate that scales with level.
I also want divine magic to be able to accelerate recovery from more serious injuries, but only very powerful magic should have an injured character fully recovered in a day.
I want there to be a limitation to how much magical healing a body can take without side-effects, but I want that healing to be readily available in combat even without a cleric, preferably in the form of single use items such as potions.
Here is an idea of how it could work. Keep in mind that the numbers chosen are meant to represent the idea, so consider them malleable. Playtesting would be required to hammer everything out.
Effects of Damage: I see there being two health related conditions, Bloodied and Wounded. Bloodied occurs when you're down half your hit points. Wounded occurs (by default), when you reach 0 hit points in addition to whatever the death and dying rules happen to be. Both impose a -2 Wound Penalty on the character, but wound penalties don't stack to prevent a death spiral. This incentivizes characters to never let each other drop to zero hit points.
Cure Spells: The Cure spells heal hit points, and can remove the Bloodied condition, but they can never heal the wounded condition. Only long term healing can do that. Say, four weeks without strain to heal naturally, half that if you have magical help. Powerful rituals or spells might cut it down further.
Each cure spell simply heals a percentage of your total HP, such as:
Cure Light Wounds: 25%
Cure Moderate Wounds: 50%
Cure Serious Wounds: 75%
Cure Critical Wounds: 100%
Limited Healing: If a character receives a total amount of healing in a single day that is more than 100% of his or her total hit points, they are sickened for the rest of that day. Penalties from being sickened do stack with the bloodied or wounded conditions. Thus, you can heal characters as much as you want, but there is a consequence.
Adrenaline Surge: Some conditions, such as Barbarian Rage, bardic music, an invigorating speech, or even a dramatically appropriate sense of desperation, cause a surge of adrenaline that allows a character to ignore pain and injury and fight with great conviction. How long this lasts depends on what triggered it, but the effects are the same. The character ignores all wound penalties and receives a +2 to all attacks. They also gain temporary hit points equal to 50% of their total.