For your own musical and health benefit, most certainly it is worth improving one's technique. It is never too late to learn something new. Can you clarify about not being taught? Do you study under a teacher currently?
Should I be worrying about the way I press the piano keys and how my wrist is positioned because I was never taught.
Yes I was taught by a teacher but unfortunately, although nice, wasn't very good. She never taught me proper fingering or any theory or technique. One teacher I went too a few days ago spent the first lessons talking about correcting technique and making sure I play every note clearly, which as you said it isn't too late and I should correct it