No, assuming by yellow book from the WHO you mean the International Certificate of Vaccination or Prophylaxis. Tampering with your Certificate invalidates it.
The Certificate does not exist for your own records. It is an official document which is used to prove vaccination (or to explain non-vaccination) when entering certain countries or regions. See the World Health Organization's International Health Regulations, 2005, which authorizes the Certificate.
The purpose and scope of the IHR (2005) are “to prevent, protect against, control and provide a public health response to the international spread of disease in ways that are commensurate with and restricted to public health risks, and which avoid unnecessary interference with international traffic and trade.”
Annex 6 of the Regulations sets out the rules for the Certificate.
- Persons undergoing vaccination or other prophylaxis under these Regulations shall be provided with an international certificate of vaccination or prophylaxis (hereinafter the “certificate”) in the form specified in this Annex. [...]
- Certificates under this Annex are valid only if the vaccine or prophylaxis used has been approved by WHO.
Unless your child vaccinations were made under the Regulation, they are not eligible to be included on the certificate.
At present only the Yellow Fever and Polio vaccines are eligible to appear in the main part of the Certificate, although there is the "Other vaccinations" page.
- Certificates must be signed in the hand of the clinician, who shall be a medical practitioner or other authorized health worker, supervising the administration of the vaccine or prophylaxis. The certificate must also bear the official stamp of the administering centre; however, this shall not be an accepted substitute for the signature.
This may be hard to obtain retrospectively.
- Any amendment of this certificate, or erasure, or failure to complete any part of it, may render it invalid.