Can I go from a 32-34DD/E to a 32C-34B? (photos)

I am sorry to hear about the problems your disproportionately large breasts have caused you. This can be especially difficult given your relatively young age.
Before undergoing the breast reduction procedure it will be very important to communicate your size goals with your surgeon. Most patients wish to achieve a enough of a reduction to help with their symptoms while remaining proportionate with the remainder of their torso.
With the goal of improving communication with my patients I find the use of photographs of “goal” pictures (and breasts that are too big or too small) very helpful. I have found that the use of words such as “natural” or “B cup” means different things to different people and therefore prove unhelpful. Also, as you know, cup size varies depending on who makes the bra; therefore, discussing desired cup size may also be inaccurate.
It is possible to reduce the breasts size very significantly. The concern with the amount of tissue removed is related to blood flow to the remaining tissue; if too much tissue is removed in one operation the blood flow to the remaining tissue (including nipple/areola) may be compromised.. Part of the tissue that is left in place is called the “pedicle"; this segment of tissue is responsible for delivering the blood supply to the nipple/areola tissue. If the pedicle is made too small (in the effort to reduce the breasts as much as possible) then patient will likely have problems with tissue survival.
The other concern with overly aggressive breast reduction surgery is patient dissatisfaction afterwards. It is not unusual for patients who have lived with very large breasts to want to have as much as possible removed. Care must be taken to be judicious in this removal to avoid an outcome where the breasts are too small in relation (proportionately) to the patient's other body parts. Again, it is not uncommon, for patients' breasts to become smaller ( after the breast reduction procedure) with time and/or weight loss- breast augmentation may become necessary to achieve the patient size goals. 
I hope this, and the attached link, helps.

Thank you for your question and photos.  Without photos of you or more importantly, an in-person evaluation of your body, it is very difficult to tell you what would best and realistic for you.  Please be seen in person by a board-certified plastic surgeon to find out.All the best,Dr. ResultsMiami, FL