Hello,
This soreness of breasts can be due to hormonal imbalance which has most probably caused irregularity in periods in your case also.
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.
I am no expert in the matter, but it sounds like you may want to take a pregnancy test.