A mild to moderate fever associated with chills/shivering and muscle aches is typically from a viral infection. most of these infections would only last for 3-5 days, but about 10-15% of these infections can last two weeks or so. Since you have had these symptoms for 6 days, this is still very likely to be a viral syndrome.
There are some symptoms, though, that are worrisome. If the fever is higher, such as 39.5-40 degrees, that would be more worrisome. It is also possible that a generic viral infection can cause a secondary pneumonia to develop, and a sudden higher fever or the onset of shortness of breath or a cough productive of purulent sputum would be worrisome that a secondary bacterial infection is developing. A slight tickly cough is common with a generic viral infection and is not a concern.
As long as you are not having any of the worrisome symptoms, it is fine to continue to manage this as a viral infection, as you have been doing. Using ibuprofen or paracetamol for the fever and aching is fine. Drinking plenty of liquids is important to maintain hydration. You say that there is already slight improvement, and there typically will be more rapid improvement over the next few days to a week or so. As long as there is steady improvement and no development of worrisome symptoms, then it would be fine to give it another week to see if it will resolve spontaneously.
If I can provide any additional information, please let me know.