Claiming child benefit/ child tax credit?

I am a South African living in the UK. I am here on an ancestry visa and have not yet applied for my indefinite leave to remain. I have recently had a baby who is a British citizen and his father is British. I am wondering if I am allowed to claim child benefits or child tax credits as it is for use on my baby and he is british. I called hm revenue and customs to see if I was eligible, they said I was able to claim + gave me an estimation of how much I could expect to receive and sent me the appropriate forms to send it to begin my claims. However, my visa states that I do not have access to public funds but I'm not sure if this is an exception as the benefits are for my child and not me and he and his father are both British- not sure how the system works... Pls help!!