Everything bad in the world is the result of original sin.
Adam and Eve had no diseases, no broken bones, were immortal.
After they sinned of course; this is when death, disease, misscarriages, pain....All things bad entered the world.
It really has nothing to do with God allowing so much as it has to do with living in a fallen world and witnessing the product of original sin.
Our lives are going to be filled with things like this because by an large we live in a fallen world.