Oh that all sounds so stressful (and I'm so sorry about the loss of your cat; we just went through that over here and it sucks, big time). I can absolutely relate to that feeling you describe. It's actually a pretty common defensive mindset for folks dealing with anxiety or depression; that idea that if you can just be prepared for the worst, you'll be protected from the effects of it to some degree. It took me a long time to learn that having contingency plans that were actually helpful was very different from always assuming the worst. Have you ever spoken to your therapist about that mindset? If so, what has she advised?
While I think it's good to be mindful of how things like depression and anxiety can effect a partner, and to take care not to make a partner ones only source of support around those issues, telling a partner about the crappy stuff going on and how you feel about it isn't automatically emotional labor. If your partner is with you, that suggests they care about you, and if they care about you then it stands to reason that they'd want to know if there are things that are upsetting you, even if all they can do in response is hug you or listen to you vent for five minutes. Does that make sense?