Can sore nipples and tender breast mean breast cancer or swelling in the breast? no period coming and not pregnant what is it?

Unlikely: It is unlikely however if it persists you should see your doctor for an exam.

Unlikely: Its unlikely to be cancer. But it could be a sign of infection, inflammation or even pregnancy. Suggest you consult your doctor who can examine you and check for pregnancy too.

Possibly: Unfortunately, I am not going to say unlikely, I have seen patients with sore nipples, itchy breasts, itchy rash on breasts, nipple discharge, tingling sensations in breast, --variations of the above, with / without pain-----go on to have breast cancer. It may not be typical, but earliest detection is a must. A "neg" mammogram and/or ultrasound does not mean you can't have ca. See specialists bx.