Few surgeons spend the time and effort to do a complete job. The muscles of the upper chest and neck form a scissors like action against the 1st rib, compressing the nerves and vascular structures between the 1st rib and clavicle. If the rib is not resected at the level of the spine it can grow back or form a mass of scar tissue which can be worse than the rib was. If the surgeon only removes the rib and fails to look for abnormal muscle bands compressing the nerves and vascular structures, the patient will only have temporary relief. Physical therapy, time, stretching, ice, and prayers will not relieve the compression of the nerves.
Heat does help to relax the surrounding muscles and ice can help to relieve the pain and swelling.
If a tree has fallen on your leg, crushed it and you are pinned underneath that log, only one thing will help. Don't cut the tree off and leave the trunk on your leg and have the doctors say learn to live with that tree on your leg. Hell you have another leg, get on with life. Learn to ignore the pain of having that tree on your leg and if it helps put ice on it. Hang in there.