My first fibroadenoma was when I was 15 and larger than a softball, so it needed to be surgically removed. Yours sounds totally fine, but keep monitering it every 6 months.
If you end up having several, recurrent, fibroadenomas it can slightly increase your risk of breast cancer, but nothing to worry about too much as long as you do your maintenance check-ups.
In regards to your kids, yes, there is a chance they too could get fibroadenomas, but as another Commenter said, they are not cancer, just a nuisance.
Best of luck.
I got my first fibroadenoma at your age. It was huge and had to be excised. Two years later another grew in the similar area and also had to be removed. Since then, I get fibroadenomas and cysts fairly regularly, but have not had any removed. I mostly monitor them. From what I have read online, yes, it isn't unusual to get a fibroadenoma at your age. I'm guessing that if your mother has the condition there is probably a chance your daughter may also at some point in her life. The good news is that they are not cancer. Mostly just a big nuisance! Having fibroadenomas may slightly increase your risk for breast cancer, but with good monitoring you should be okay.
Good luck and try not to worry too much. I know how it feels to be your age and have something strange grow in your breast.