I don't think it's necessary to be overly explicit with what the problem was unless you want to be. However, I think something along the lines of "hospitalization for a life-threatening medical issue" should definitely be included. And if it was emotionally traumatic, as I can only presume it must have been, be sure to include that too.
I'm so sorry you went through such a tough experience. Thank goodness you are well now!
Life hits all of us hard once in a while. It's inevitable that we're going to falter a bit. We're only human. If you could go through something as traumatic as what you endured, and be completely unaffected by it, what kind of vet would you be? I'll take the vulnerable, authentic you any day.
Just my 2 pennies.