How do I ask My Overprotective mom for an instagram account?

Tactfully.
It really depends on your age.

I am 12

Why do you want an Instagram account? How will it improve your life?

Meanwhile, are you a wonderful child, helpful around the house, who does chores without being told, always a smile on your face and a song in your heart?

The age for membership is 13, so you need to wait a while yet.

Yes I will take out the trash I make my bed I make my parents bed I walk, feed, and bathe the dog I clean my room wash the dished set the table etc. without being told I am always smiling and if you want me to do a chore you only have to ask me once
It won't improve my life one bit really except my mother lets me have almost NO social life (with friends)

Oh well... I may still try if I can work up the courage... It can't hurt to ask can it

Well, you're not old enough for an account, so continue being a wonderful, responsible son and be patient.

Will do
Ps I am a girl