So I sweat ALL the time?!....?

Basically it sweat even when its cold. All my classes in school are cold, yet i still sweat through my shirts. I ALWAYS put on deodorant before school, but it doesn't seem to help. I've even tried switching my deodorant, and nothing seems to be working.

Another thing is, I'm always cold. Maybe i have bad circulation? i don't know. My hands are always cold, and so are my feet. I always have to wear socks around the house and at night, cuz they are icicles when i wake up. Sometimes they are so cold it wakes me up in the middle of the night. Even though my hands are cold, they rarely sweat unless I'm nervous. It also seems that my feet only sweat when I'm wearing shoes with no socks. hence all my flats smell really bad, but my sneakers are fine.

One last thing, my nose is always cold too. Yet my face is greasy, and so is my hair. I shower every day, but it doesn't make a huge difference, because my hair is greasy again after it dries. I don't use conditioner, because it makes my situation worse, and I've also tried switching shampoos with no results. Its hard to find a good shampoo, though, cuz i have dandruff, and greasy hair, so i can't use shampoo for dry or oily hair.

I know this might be because I'm a teenage girl, but i have been for 3 years now, and it only started this year. Ive also had my period for 3 years. My thyroid is fine too. I don't have a high or low metabolism, and i do eat healthy foods. The only thing i can think of is that i don't drink enough? maybe like 3 pints a day. But i never feel dehydrated, and am never thirsty after what i normally drink. I also never get headaches.

My mom is a doctor, and is fully aware of everything, but she is as stumped as i am. she said maybe getting a prescription deodorant? i feel like theres more than one problem though, if sweat is not the only issue.

Please add some insight! i want many peoples opinion, and please don't just write one or two sentences. Thanx!!!