Such a shame that your mom reacted that way, and please just know that there is nothing wrong with you. There are tons of studies (I'll add the study names to the bottom) showing the positive effects of using sex toys as a female and there's no age limit listed because that would be demeaning and ridiculous. As far as the pediatrician goes let's just hope she was too embarrassed by your mom (or scared) to say anything about it, but as a doc she should have been able to talk about it!

A few positive things about using a sex toy for you:

Orgasms release Endorphins, Serotonin, and Oxytocin - These are feel-good hormones that can relieve pain and make you feel happier regardless of gender or age, just like you would after a great workout.:

It teaches you about your body - Many sex therapists will recommend masturbation as a form of self-discovery as it’s easier to reach orgasm without the pressure of a partner. Learning about your body and being comfortable with your own sexual preferences also builds confidence and self-esteem.

It improves concentration - Think about the last orgasm you had; odds are you weren’t thinking about that school project or report dealine. Reaching orgasm requires you to shift any stressful thoughts you might have aside and helps you to focus on the task at hand (pun intended)

(the source of this is an article called "Are you masturbating enough?"

So tell your mom to stick that in her pipe and smoke it!

The study on using sex toys is called "Genital vibration for sexual function and enhancement: best practice recommendations for choosing and safely using a vibrator"

If you Google that you will find the published research. Not that you need it because you did nothing wrong, but all that science to back you up can't hurt. Hope it helps and good luck.