I get upset by the slightest thing. I do sympathise.
Whilst I can't help how I feel, I can help how I act.
Even if something (for example, something someone has said) has really got to me, I don't show it. I try to keep my dignity as best as I can. I recognise my hypersensitivity as a failing on my part.
The old saying, "Least said, soon mended" often applies. I would generally avoid the person who upset me and get on with my own business. There's no real point in having it out with them, as it's often a case of me making a mountain out of a molehill. If I say nothing, then I've nothing to feel bad about later on if I run into that person again. How they made me feel would remain private with me. This is particularly useful advice if you work or interact with the person in question on a regular basis.
The pain soon passes and life goes on.
But, if it was something really important, then that's another matter...