When should i wear the bra?

Yes, you need to wear it. It's important. If not, your breast may look bad in future! It will affect your back bones too. (you know, breasts are heavy!)

Also, you are almost C cup! Without a bra, your breasts will be obvious even after wearing two T-shirts. It's inappropriate.

And you are 13 already. Totally appropriate.
You may go to a bra shop with your mother or female relative (auntie etc) and pick those that are comfortable. I suggest you choose the ones with simple patterns
and light in colour because you need to go to school and they won't look obvious
under your uniform.
(really! imagine a black bra under a white or yellow uniform dress)

Remember, choose those that are comfortable! Better consult your female relatives the first time you get a bra.

Yea, you should wear bar right now. When you feel that your breast starts getting bigger and bigger or a little bit painful.