I kind of had to stop "considering myself at all" when I hit 60 (aka "37" in conversations with my kids, who have been familiar with my joke for quite some now). It was kind of mind-boggling enough that I just didn't think about it for the first year. The second year I had to not-think about the fact that I was the age my father was when he passed away.
The third year after turning 60 I'd been in my sixties long enough to have learned that there's little point in thinking about it at all. I know I can't consider myself, "young". That would be ridiculous. I don't consider myself, "old", although I know there are more and more people who are younger than I am who would. And, it kind of irks me that there are people my age who also would/do consider me, "old". The former group will learn better with time (or not). The latter group has a right to their own thinking for their own reasons, but I'd rather they not lump me in with them. :/
Any health concerns that I have have nothing to do with my age. In fact, I'm fortunate enough not to have (knock-on-wood) "joint type aches and pains". I feel the same now as I did at 30 (and in some ways, at 3 or 6 or 20 or whatever...). I know more, which is good. I don't look as good (needless to say,), but I wasn't fashion model material when I young either, so what's a little extra self-conscious-ness and a little more "not-being-all-that-thrilled-with-my-looks" at this stage of the game....
I suppose I worked out that I would consider myself, "late middle age" for another while. I've always had a lot of respect for "old" people, so I don't necessarily think "old" is a bad thing (the way some people) do. I just don't feel old yet. At this point (and unless/until something changes for me), I've worked out that I'll probably start calling myself "old" once my hair is all gray or white (for now it's neither). We aren't defined by our age (which is why I've also always had a lot of respect for anyone younger than I am; just as "old" isn't necessarily a negative thing, "young" isn't always a positive or negative thing either.).
So anyway, I'm good with calling myself, "late middle age" (for now and the immediate future). It's too bad that people over 50 don't have their own version of a term like the one used for kids of a certain group, "tweens:".