wondering if maybe a baptism record is available all she knows in the childs name and dob being jan 1957 and death in june anything i can look for notices in newspaper ect
Some people placed birth and death announcements in local newspapers. Unlikely to have been a birth announcement if parents of a child weren't married.
For baptisms, you would need to know religious denomination + the area where the child was living or staying when she was baptised so that you can identify what churches were in the area at the time.
If the baby died in hospital, it's possible that a baptism was performed by a hospital chaplain.
Some baptism registers from that decade have been deposited in archives, (Lancashire Archives or Manchester Libraries & Archives) some haven't. E.g. a register of my family's church with 1950's baptisms is in Lancashire Archives but the baptism register immediately preceding it hasn't been deposited there.