Word for something that doesn't kill you but makes you stronger
Solution 1:
1. I've been through a lot in my life and turned me into a fighter.
2. The experience determined the very things that didn't kill me but made me stronger.
There are connotations here of ORDEAL, TRIAL, TESTING, and of a process of distillation, in the sense of separating or extracting the essential and vital elements within, and of a refining process, in the sense of being purified of what is coarse, debasing, or superfluous, again it is a reduction to what is essential, vital, true and strong.
This is the purpose of the alchemist's retort, and of the crucible.
3. These ordeals were my crucible."
CRUCIBLE noun: 2. a. An extremely difficult experience or situation; a severe test or trial: "the emotional crucible of a wartime deployment" (Kristin Henderson). See synonyms at trial. see, The Free Dictionary
Solution 2:
I'm not sure if there is a word that means that specifically, but it can always be inferred using other terms.
One that springs to mind is foundation.
The experience determined the very things that didn't kill me but made me stronger. These things are my foundation(s).
This suggests it is the deepest thing within the personality, which is then built upon, which will likely imply it was caused by something deeply profound (such as a near-death experience etc.) You then may need to elaborate, but I think it would be understood what is meant from the context.
You can use other words like inspiration or motivation, but I don't think they quite have the gravitas that you're looking for.
Solution 3:
Just to niggle, it's more of a famous quotation than a proverb, though you could argue that it has, alas, become one.
For your short phrase, you might go with 'fate' and I think sick old Fritz might approve.
I have problems with your experience "determining the very things". Might I suggest cutting out the middle altogether, and run straight from "I've been through a lot in my life and it turned me into a fighter" into "This was what failed to kill me but made me stronger", or, using the quotation more verbatim, "This was the 'whatever' that 'did not kill me but made me stronger'" Just my ten rappen.
Solution 4:
I was going to suggest inoculation
. I had guessed that the etymology was related to 'noxious' -- a poison -- that made you stronger.
Upon research that derivation turns out to be incorrect, but I think it is still a possible answer, even if it is a bit metaphorical.