I can relate to this. I'm a big problem solver-y kind of person and that means I'm very good at logicking my way out of feeling bad, like you are. It gets tricky when it's something you can't fix that way though. Personally, I found that I had become so reliant on my problem solving skills that I had a poor ability to cope emotionally when it was just a shit situation I couldn't do anything to fix.

For me, one of the steps towards coping better with that kind of stuff is stopping trying to logic through something if that approach wasn't working. Don't beat yourself up about "irrational" upsets. Feelings don't care about the facts and even if your feelings are irrational, it doesn't help to be exasperated at this. That can often strengthen them.

Once you've accepted that you feel shitty and it's valid and okay to feel like that and not have a way to fix things, the next step might be taking time away from the stressful thing, or giving yourself some random treat completely separate from the sad thing, or venting, perhaps to a friend, or even a journal. What helps you will depend on you and your particular situation, but step 1 is to let yourself feel that weight on your chest. How much something hurts isn't based on any objective standard, your struggles' validity don't depend on rationalising the thing that upsets you.

Things suck right now for you, but it's okay to not be okay.