Your injuries are pretty spread out because you suffer from both neck and back pain. How long it takes to heal will depend on how severe your injuries are. Back pain may take up to a year, whiplash should probably be recovered from within three months, or the neck injury may be more extensive and may need further exploration.
I would say that you should give it at least another full month. If you have not improved significantly, then you may want to seek further care.
However, at any time if you feel that your needs are not being met by the doctor that you are seeing, it is always advisable to seek a second opinion. Since you are seeing improvement, I would say that there is probably no need to change doctors yet. Had your doctor given you a timeline for recovery when you began your treatment regime?