Could a tight bra (the rough ones not soft) cause neck pain?

Neck pain. Large breasts rather than an uncomfortable bra is more commonly the cause of neck pain. In my practice, I will refer patients to plastic surgeons for a breast reduction procedure to eliminate the neck pain when other nonoperative measures have failed. If you are physically uncomfortable then you can get neck pain due to muscular stress. So go to a specialty bra store for a comfortable fit.
Neck Pain. The tightness of bra usually is not related to neck pain. You should wear a bra that is the proper size and support for you. If you have heavy or large breasts, it may effect the back muscles and in time with improper posture and constant attempt to compensate by holding your head up and straightening your neck, it may effect your neck muscles. You may try a different bra or no bra.
Depends. it depends on the size of the breasts. Large breasts is a potential cause of back and neck pain. Do you feel less discomfort if no bra or loose bra? Then the answer will be obvious.