My ex is telling people my child isn’t his?

My ex has told his family that i sleep around and my unborn baby is not his. I want to get a pre natal dna test done because i want to prove him wrong. I feel like i should wait until i have the baby but my due date is in June and i want to clear my name
I can’t wait until June for the dna test. Am i being childish or not?
My ex is telling people my child isn’t his?
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