It is scary all the things that can happen to them. I loss my sweet Annie suddenly in March and was unbelievably blessed to get Gracie just 2 weeks later. It's July and I'm only just now getting a little less anxious.
Two things I learned, 1) you do the very best you can and let God take care of the rest. 2) stay away from the "Sick/Injured" discussion group.
I was making myself a basket case reading about all the stuff happening. I offer up a prayer when I see it asked for in the title, but I often can't read the thread because I was upsetting myself. I figure by next year I'll be able to handle reading them.
Take a deep breath, let it out, relax and enjoy the incomparable joy these little angels give us.