There is a whole tear thing that I've heard of, sort of in the opposite direction, re people who cry too much (I gather) and an abused person I met with my relations with people in northern california. There are even treatments for that, I heard. Dlowan knows the pros and cons on this, I think.
I'm not a psychologist. I'd just say cry whenever it happens, get in touch with your cryer. Or at least don't reject that as something to do.
You will also note that culturally boys are primed not to cry fairly early on.
I've no idea if this is a horrible imposition on boys, or what.
I do know I liked it when I saw my husband cry once in a while, from sorrow. That meant he wasn't the magic mask.
But crying right away in your instance, I can see not. Don't beat yourself up. Natural reaction, maybe related to adrenalin, etc.