Im 12 and I still don't have my period! Although some of my moms friends daughters are as young as 7-9 years old and have gotten it! Every girl gets it at a different age, but I reccomend you have some pads or tampons ready in your schoolbag/locker just in case.
I also reccomend you talk to your mom/aunt/grandma/etc. about what their period was/is like. They could also give you good advice on how to handle it.
I do think you should make yourself an Emergency Period Kit though, because you never know when they will start. Some examples of things you could keep in the kit could be:
Tampons\pads (whichever you use)
Water
Change of pants/shorts
Change of underpants
Tissues
Snacks
In terms of bringing pads to the restroom, I wouldnt worry too much! You could always use a pocket or just grab one from the nurse if you run out! Besides, even if people see you with it, especially other girls, they prob wont judge you too badly because I bet some of them are experiencing it too!
Also, even if you are experiencing a lot of the common period symptoms, its important to remember that it doesn't mean your period is coming super soon. Everyones period is different, and some are heavier than others. I have a lot of the common symptoms as well and I still haven't gotten it.
I hope this helps! Good luck!! :)