It is entirely possible that you suffered a mild internal injury that you weren't really aware of at the time when you had your accident. This is fairly common, particularly injuries of the neck. When a person is involved in a motor accident, most of the time, the neck gets jerked really hard. One of the commonest things that happen is a whiplash, which can easily skip being diagnosed unless you repeatedly complain about it and a doctor examines you for one. Of course a whiplash is not something you'd be likely to miss, so you'd probably have noticed it right away. In all likelihood, your head must have been jerked hard and you have pulled a nerve, tendon or muscle in your neck as a result of that. The relation to the coughing is that each time we cough, we involuntarily jerk our neck decently hard. And this can aggravate an already aggravated injury a lot. So in order to ease your situation, you need to adopt a two fold approach. The first thing is that you need to get your neck in a brace so that each time you cough, it is not thrown about. The next thing is that you need to work towards getting rid of your cough. Once you are rid of the cough, you can work towards taking care of the pain in the neck.
To ease off the cough, you can make a mixture with equal parts of honey and ginger juice and keep licking it on and off during the day. This will help to soothe your throat and will also help to get rid of the cough. You can steep a hot tea with a few peppercorns, cloves and a cinnamon stick and have this while it is hot. It will provide relief to your throat and will also help to loosen congestion if you have any. A couple of days with these remedial measures and you should be easy on your cough. Meanwhile, you should gently apply a thin layer of mustard oil to your neck where it hurts the most and then apply a warm compress over it as well. Try not to massage, as there are some injuries which can actually turn worse if massaged. There should be no application of pressure. If the warm compress does not work - you will know in a couple of days - then you should switch to using ice compresses.
answered by G M