The answer is no.
There are multiple ways our bodies ensure that we have a unique set of DNA that differs from our parents. For starters, you inherit two copies of each chromosome—one copy from your mom and one copy from your dad. This means that your genome (all of your DNA) is already different because it contains chromosomes from both of your parents. This can also help explain why two siblings appear to have different genetic ancestry, since they may get different chromosomes from their parents.