No, it makes you normal. Your exhaustion has no implications for your love for your children, or your maternal abilities. Hang in there — it gets better. In the meantime, ask for help. Have someone (your partner? your mom? a friend?) take over baby duty for an afternoon while you sleep between feedings. Also ask someone to go to the grocery store for you, or to cook. Seriously — take advantage of all the help you can get. You deserve it.
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