Hello from JustAnswer.
There are several considerations when there is a persistent cough with no evidence of infection or a failure to respond to antibiotics. It can be related to non-infectious inflammation of the airways, which is most often due to allergies or irritation by a substance inhaled into the airways. The most common inhaled irritant is, of course, cigarette smoke, but most people that smoke and develop a chronic cough are not seeking an explanation for the chronic cough, so it is more likely that you do not smoke. Another common problem is acid reflux, because small droplets of stomach acid can be very irritating to the airways. Many people with acid reflux will also have heartburn, but since irritation of the airways can happen with small amounts of stomach acid, some people will develop a cough without any heartburn.
The tiredness is non-specific, because it can occur with any condition that causes chronic cough or irritation of the airways. The muscle soreness is also non-specific, because chronic cough will cause stress on the muscles involved in coughing, regardless of the underlying cause.
Although there are some tests that can be done for allergies and acid reflux, another approach would be a trial of medicine oriented towards relief of each type of problem to see whether the symptoms improve. An over the counter oral antihistamine may help to ease allergy inflammation. Similarly, there are over the counter medicines that suppress stomach acid, such as ranitidine and omeprazole, that may help acid reflux. If you try both at the same time and improve, then you will not know which made the difference, so it is better to try one treatment at a time.
If I can provide any additional information, please let me know.