Yes, it's totally a "thing" and pretty common. If you're feeling depressed, it can happen even if you're able to express strong feelings when you're not depressed.

If you grew up in a family where you weren't allowed to express anger and maybe weren't allowed to have certain thoughts or feelings without being told that "no, you don't like that" or "no, you don't feel that way" then when you become an adult and someone confronts you with strong feelings or you have strong feelings that you need to express, you often will "freeze" and start crying and not be able to say what you want to.

I think your writing is a very good idea, and it will probably help you to learn to express what you're thinking in the moment when it's happening. I give your family credit, too, for being willing to read the notes. Some families wouldn't do even that.

In my experience, it takes a lot of practice to learn to express yourself when in the presence of strong feelings if it's a problem for you. Years and years in my case, and I still can't always do it.