Unless the baby or toddler is infected with some known Virus that could be spread through contact through the Urine or Feces then you're unlikely to get sick from changing your babies diaper.
Just be sure to wash your hands and your babies hands after changing the diaper especially wash the toddlers or babies hands if they touched their poop while changing the diaper.
If the baby is sick with some Virus then you might want to wear gloves while changing the child's diaper like the daycare centers are required to do.
But other than that no you shouldn't get sick just from changing the diaper unless you didn't wash your hands and then touched food.
Many parents change diapers daily and don't get sick from the diaper changing even when they don't wear gloves.