What could a sore hard breast mass be other than cancer?

Possibilities...: ...Include a cyst, a tumor (benign or malignant), or fibrocystic changes. Any new breast lump should be evaluated by a physician to be certain that it's not a cancer. This certainty can be reached by physical examination, mammography, ultrasound, and/or biopsy, depending on many factors. If your doctor is certain that the lump is not cancerous, it does not need to be removed.

Different things: Cyst, abscess/infection, benign tumor like fibroadenoma, lipoma, lymph gland enlargement, fibrocyctic changes, milk cyst, hematoma/blood accumulation from trauma etc.

Yes: Could be a cyst, a benign tumor called a fibroadenoma, or an infection. Breast cancer in a 20 year old would be exceedingly rare.

A variety: of things: benign tumors such as fibroadenomas, inflammed cysts, abscesses and focal inflammation, fat necrosis, diabetic mastopathy, hematoma, to name a few. If the answer is not clinically evident, or specifically benign on imaging, biopsy may be necessary to make a determination.