Kind of maybe what you're looking for?

All Over the Street

On second thought, it might very well be Water is Another Matter

Again, I apologize for the delay here! If anyone’s interested, here’s Triage. I can’t say I’ve read it myself, but it comes highly praised, and from what I can tell, it looks well-written and interesting. (Please read the warnings for it!)

I have to say, even after some pretty extensive google searching I wasn’t able to find too much that really fit what you were asking for.

Only The River Variations seemed to be the only fic that was at least somewhat plotty and long in which John got critically injured, Sherlock freaked out. That being said, I can’t say for sure that this fic matches your request exactly (although I hope it does) because I haven’t read it.

Here are some others that slightly fit the request:

It’s Not The Violin

Nobody’s Fault But Mine

I Feel a Weakness

Protective!Sherlock happens to be one of my favorites, so I most definitely do.

Water is Another Matter (This is by cathedral_carver, and it's a fandom favorite!)

26 Pieces (Another fandom favorite!)

Man and Beast (I highly, highly recommend this. Absolutely one of my favorite AUs ever. Very protective/possessive Sherlock here).

Obsession, Appassionato (Possessive/protective-ish smut).

Entropy 

Bedside Manners

Reassurance

Opposites Attract

Love Is The Rhythm

Protective and Possessive

That's all I'm putting down for now, but if you want more, feel free to ask! I've tried to find a nice mixture of genres and lengths, as protective!Sherlock can be in all sorts of fics. I do have a protective tag that I recommend looking through (be warned that it also includes protective!John). I've recced my absolute favorite prot!Sherlock fics from there here, but there are plenty more good ones in the tag. Hope you enjoy these! (MATURE READERS on some of these, so check the tags/warnings, please!)