I personally met a woman who did exactly that in the 60s. Her baby was born at home in Honolulu. She took the baby to the doctor for a check-up and the nurse told her to get a birth certificate.
She went to the county, told them when and where the kid was born (no attending physician) and got a birth certificate a month after the kid was born.
She could have said anything. It didn't matter.
Following their trip to Hawaii, the investigative team saw that national security implications were more compelling than whether Obama’s birth certificate was legitimate or not. Arpaio’s team found it was a false and modified document but that this matter now needs to be handled by Congress.
I had not read your story before. Perhaps if you set all the facts, including the who, what, when, and where of your story, it may be useful in the coming days to other investigators. Just a thought.