If you are referring to eCitzen portal account, then kindly note that you cannot apply for someone's child a birth certificate using your personal account. One of the parents has to use their eCitzen account to apply for a birth certificate.
You might want to visit Huduma Center to correct the error.
Regarding your second question on whether you need to take the form to Huduma Center after applying for a birth certificate online, it is not a requirement. However, you can take the invoice to Huduma Center for a follow-up if you want the process to be faster.