Is it bad for my 15 year old sister to wear a 34h bra cup?

As long as it fits: A bra should fit well & give good support. Some 15 year olds are under 5 feet tall, while others are over 6 feet, so a teen girl needs to wear what fits well. With very large breasts, she should see her pediatrician for an exam and advice. It may be good for her to work out and develop very strong back and abdominal muscles, so the breasts won't cause her back pain or other symptoms in the future.

Unusual but not rare: Although this is unusual, it is not rare. In instance where it is associated with lactation, then a hormonal evaluation may be warranted. If this persists, she may benefit from a breast reduction.