You may approach ICA to obtain a copy of your child Birth Cert if he is born in Singapore whereas for the health booklet, you may refer to this link https://www.healthhub.sg/programmes/125/children-health-ehb or approach HPB
some detail are here - https://community.theasianparent.com/q/i-t-find-child-health-booklet-birth-certwhat-i-should/732517
TapFluencer
u can download the healthhub app and it will show the list of vaccinations your child had.