I am so very sorry! I wish I could give you a hug. I know how important an animal is in our life. It sounds as though you love animals. Be proud of all you've done to make their life happy. You've done nothing wrong when you lose one- that is just nature. It is never your fault. You've helped give them a happy, safe life. Be happy with all you've done to love them!
Yes guilt can totally give tms symptoms I'm sure. That is one of my struggles on healing this too. Try writing why you feel guilt. Hopefully it will reveal how there's not really anything you should feel guilty about and will help you release it.