Can I get sick from my child's vaccinations?

Not usually. Most vaccines are "killed"; as such one cannot get sick with the illness nor transmit it. A few vaccines are "live attenuated", such as mmr, varicella (chickenpox), and nasal influenza vaccine. One could potentially get sick if severely immunocompromised, such as aids, cancer on chemotherapy, or organ transplant. For most individuals, exposure to a recently vaccinated child poses no risk.