Children born with birth defects or HIV did not have much choice, didn't they? What sin did the newborns commit?
You make as much sense as a hippopotamus explaining Shakespeare.
Newborns clearly have not sinned. They may suffer however do to the choices made outside of their control. Children born with HIV are suffering because of the choices of the elder generation usually their father or mother. Human choices do harm the innocent.
Children with cancer are dying because a part of them has broken away and defected. It no longer acts in its assigned role for the greater good but instead strengths itself over the short run via unrestrained growth. Left unchecked that growth will eventually disrupt the delicate balance necessary for life and will end in death.