1) Don't pursue 'fashion' or high end brand names. At your age it is a waste of money and someone will steal it. You are there to study so grades are what matters more than anything.
2) Even if your grandparents are kind enough to offer to help, do not take advantage of their kindness. Explore discount malls and stores in your area.
3) As for a winter coat, any down-filled parka with a minimum 450 fill will get you through with a few layers on under it. If you don't want down, then any thick synthetic fill will work. Make sure the outer shell of the coat is of a durable fabric, you know, something that won't tear easily. There are dozens of makes to choose from. Buy one with a hood.
You didn't specify your location or budget so if you will disclose this information and specific needs, we can help you further.