I'm DMing a modified version of LMOP for a group of 6 people.

I'm attempting to write their backstory into the campaign and one of them is a God of Knowledge Cleric that specialises in Healing.

Their backstory is that she was exiled from her church for failing to follow the tenets set by the head priest. A corrupt leader of a church handed on a silver platter that can come back and wreak havoc on the PC to make them feel like the star of the story = happy DM. 

The head priest is about to show up at Phandalin at the request of Harbin Wester so I'm trying to square away this backstory:

Late one night, a young man was brought to the tavern – a survivor from an orc raid. His injuries were extensive, [she] doubted whether she could heal him. But his bones set easily, and the dark magic that wounded him lifted after a single incantation. [...] As the man recovered, he offered to pay her according to her role at the temple – after all, she wasn’t a jumped-up midwife. But [she] refused, saying that she couldn’t charge a man who had no gold to begin with. In a flash, the young man dropped his disguise. The head priest stood before her, his rage and resentment palpable.

 I thought that the above paragraph could be waved away with a Disguise Self spell. However, the spell explicitly states that 

The changes wrought by this spell fail to hold up to physical inspection.

The main hindrance to me doing some distracting-hand-waving and glossing over it is that this PC is descriptive in her actions/role-playing.
Lots of "I push apart the papers on the desk and open drawers and check for hidden compartments" when investigating or "I take some of the rope in my backpack, wrap it around their leg to make a tourniquet, and place my hands on the cut to cast Cure Wounds".
So a spell that doesn't pass a physical inspection isn't going to cut it to pass muster here. 

Does anyone know of a Disguise Self like spell that could work in its place?
Or have any other idea how to manage this?

Do you even need a spell to pretend to be hurt? Maybe some pig's blood to fake your blood, but.....

True, and if one of the PCs did that, I'd just let them roll Deception and be happy out.

The way that the PC worded her backstory though "his bones set easily" makes it seem more extensive, plus the fact that she's specialised in healing.
I'll have to keep pig's blood/manual trickery as a final resort.

How about Alter Self? It is a transmutation spell instead of an illusion so you could alter your appearance to be wounded version of yourself and then when a cleric heals you, you drop the concntration on the spell and your wounds vanish, hey presto a successful healing has taken place.

Well the simplest answer is that NPCs and monsters are in no way bound by the rules and features available to player characters. The priest could know a spell that does exactly what you need and that's that.

Yes,it's called feign death

Thanks, y'all.

Alter Self seems to match all the boxes I need - in the end, I created a homebrew magic item that allows the wearer to cast Alter Self twice a day when attuned.

Covers the backstory description, the physical interaction that the PC would have done, and gives the possibility that the party may acquire a magic ring in the future.

Cheers for helping to figure this one out!