Is it weird if I do not know my actual birth date?

My mom says that when I was born, the nurse smudged the numbers on my birth certificate so when the government processed my birth certificate I was registered as being born in a different month from my actual birth date. I posted about this online years ago and somebody said, my mom could be lying about me being born in a different month from my birth certificate to hide the fact that she got pregnant before she married my dad. So now I don't know which month I was actually born in.

Is it weird if I do not know my actual birth date?
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