If you're having that many big expenses that often, it sounds like in some sense they aren't really "unexpected". You're going to have to plan for expenses at that level in your budget, somehow.

This is typically what insurance is for. Perhaps it is time to improve whatever medical insurance you have to cover more (probably at higher premiums), and look into insurance for your pets (which is a thing that exists I hear, although I don't know much about it). Sufficient insurance would at least take the "surprise" out. Earning more to cover the increased insurance premiums isn't really something anyone here can help with -- it sounds like you need to somehow increase your income or reduce your expenses further or both.