Well it's normal to get really emotional when you don't feel understood. Situations like that still frustrate me to no end, but I have to remind myself that they just don't know, and why would they. The "oh I stutter too" comment is common, so it's important to mention that it's a speech impediment. And the fact that you stutter less when you "own" it like you said is so cool. Makes you feel kinda badass and builds character. Good luck with everything!!