Not necessarily.
While I'm not a physician, I don't think that it's normal for the nipples to be sore because the breasts are growing, and there are plenty of other things that could cause them to be sore.
It could be an indirect result: larger breasts might "bounce" more, causing the nipples to rub on the inside of your clothing, which could in turn make them sore.
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When your breasts grow rapidly, they can ache. It's because the skin and muscle structure on your chest haven't had a chance to stretch out and accomodate the new breast tissue.
A bit. They hurt more when you begin to have your period. I always had sore breasts as part of PMS each month.
As a man I can say yes anything that's growing on your boti hurts a little bit but it's real painless for them but you will find the most pleaser in them whin a man or girl is playing with them