If you weren't worrying about the vaccine, it would be something else. As it happened my youngest had rotavirus as a baby, and it was nothing more than a week or two of green poo. Mine all had chickenpox without incident as well, other than lots of spots, wall-to-wall calpol and six delightful weeks of having Madagascar on a running loop.
As they get older, there are other things to worry about - stuff that happens at school, are the teachers supporting them properly, are other kids being horrible to them, are they going to catch illnesses of other kids. And for teens, are they crossing the road sensibly, are they being influenced to try drugs or cigarettes or alcohol, are they going to fail all their exams?
Do you see what I mean? There are always thigns to be anxious about - as the line goes, once you've had a child there will always be part of you walking around outside your body, vulnerable and unprotected. So the task of adapting to parenthood is finding a way of managing that anxiety without letting it destroy your ability to take pleasure in the present. Ultimately if you don't find a way of reaching an accommodation with that fear, it will steal your enjoyment of your daughter's childhood, and you will find it harder to help her in turn find a way of embracing life's challenges, whether it's going on a long DoE expedition in the mountains, or facing the risk of failure in applying for jobs or universities.
Can you try and imagine what you would say if it were your daughter who had just had her first child and was feeling like you are? Would you say, "Yes, you've ruined your child's life, everything that goes wrong is definitely your fault." Or would you say, "Look, this is scary, you've never done this before, you're bound to feel worried, but small babies are very robust, and have a tendency to thrive under much more hostile conditions that a 21st century western home. It'll be fine."
I'm guessing it would be the latter. And hopefully you would also see that your hypothetical daughter's fear is less about reality and more about PND that hasn't been properly treated, and you would encourage her to push for proper specialist help.
And that is what you should do for yourself, it will help your daughter much more than obsessing over the very remote possiblity of her getting a specific illness. Your thought patterns are not normal, and there is help available, Please try and find it. 