Hi Hearty! Well, could be a side effect of whatever meds you're on, sort of an allergy thing. Closely read those printouts the pharmacy attaches to your bottles bag. But ALSO, for me, as unrelated to adrenal issues, I had chemotherapy (cancer), and afterwards, my left eye waters all the time, and same thing happened to a close blood relative of mine.
For whatever reason, it doesn't bother me too much, I just let it run, brushing it aside occasionally. But if it bothers you a lot, and it's not a predicted side effect, talk to your doc and perhaps a medication change would be good. OR you could just buy some very nice, soft linen hankies, hand-embroidered with whatever design you like, and keep it with you whenever you're out and about, like in your purse, or you can use a very simple pin, even a safety pin, and attach it to your top somehow (women used to do this about 100 years ago, for whatever reason). Gail