Hi, thank you for your question. Please rate my answer if you are satisfied. Well, it appears to me that you have been coughing for quite a while. The muscular pains as a result of chronic coughing are common, especially when you have a disease (chest infection in your case) that already has made you weak. Having said that, you may also have weak bones which make it easier to get back pains with straining (like coughing). As you mentioned that your back muscles start to stiffen if you stand for some time, that also shows that your muscles (and bones) are not that strong. Along with the treatment of your chest infection, you should also take some supplements (calcium n vitamin D for bones, vitamin B12 for muscles) and you should improve your diet (eat good quality protein, carbs and enough calories every day). And for the back pain you can take a simple muscle relaxant and pain killer (tizanidine + diclofenac).