(((((((((Peppermint_Patty))))))))))))))
Nobody here can diagnose you, but I just did some websearching, and it does say that depresson can be a symptom of hypothyroidism. It could be mood swings due to perimenopause or another medical condition as well, it could be just the stress you're under as well (since caring for anyone can be stressful as well as other things you've mentionned).
Have you talked to your doctor about the mood swings? Can you go see a therapist to talk about the stresses you're currently under, or perhaps get a referral to see a pdoc to prescribe something?
Wishing you well, take care of yourself.
Welcome to PC

Keep posting!