I'm 19 and I've always had big areolas, I hate the way both of my breast look, would I qualify for a reduction? (Photos)

It's certainly possibly to reduce the size of large areolae, and the operation can sometimes even be done under local anesthesia, for the right patient. 

The difference between breast reduction and breast lift is the amount of breast tissue that is removed during the procedure. The more tissue removed, the smaller your breast cup after the operation. An insurance paid breast reduction has a minimum amount of tissue to be removed. One common number is the removal of 600 grams or so to qualify. I doubt you have that much to give up and keep a reasonable breast size. I suggest you consider a breast lift with or without breast implants.Always speak with board certified plastic surgeons....

I would suggest an areola reduction +/- a breast lift to help improve things. I don't feel that a breast reduction would be in your best interest but that depends on what you want to achieve. you need to see a PS and run through the pros and cons.