If you are replaced, this isn't your birth chart. Your birth certificate is for the child born to your mother on that date, and the resulting birth chart is hers. Yours, if you really are that child, but to follow up with your belief, let's suppose you're not.
If this was a case of the hospital mixing up babies (happens more in fiction than in life, but it's not unknown), you might have been born the same day, but not necessarily at that time, or you might have been born within a day or two. That would give you a similar birth chart, but not exactly the same. Your Moon placement could be different. Your MC/IC axis, which is also used to indicate parents, would almost definitely be different.
Even if that birth certificate really is yours, there's still the likelihood of a rounded birth time to consider. You could easily have your MC/IC in Sagittarius/Gemini instead of Capricorn/Cancer. That would paint a different picture of your parents.
Or, let's say you were secretly adopted, and a birth certificate drawn up for you to make it look like you were born to your adopted parents. In that case, your real birth information could be quite different. Depending on the circumstances of the adoption, even your birthdate could be a guess.
There's also another possibility, that would account for you looking differently from your family but would not mean you were replaced: your mother really did give birth to you, that birth certificate really is yours, but your father isn't really your biological father. That could account for some feuding, too, if it's known or suspected.
One last possibility comes to mind: could your parents have used assisted reproduction to conceive you? If donor sperm and/or donor eggs were involved, you could be born to them but not their genetic child. That's the kind of thing that might very well be a tension-causing family secret, if they felt they needed to cover it up.
