There are many causes of soreness of breasts,premenstrual syndrome and pregnancy being one of them.Other important causes are fibrocystic breast disease,ductal ectasia,mastitis(inflammation of breasts),galactoceles,benign and malignant pathologies of breasts,referred pain from liver or musculoskeletal system,arthritis of the ribs,costsochondritis and inflammation or sprain of pectoralis muscle.
I feel that an examination by a gynecologist will be the best.Till that time,apply some warm compresses on the breasts and take some over the counter pain reliever(analgesic) like ibuprofen or diclofenac.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing