I am also suffering from what you both believe to be muscle strain from coughing. My nurse said you can take as much as 600 mg of ibuprofen at a time and can also take tylenol at the same time, as they are different active ingredients and don't interact with each other. As for me, tylenol doesn't seem to work, so I just take the ibuprofen. She also suggested alternating ice and heat (neither for more than 15 minutes), since both can help. I tried that and it works okay, I only tried it a couple of times though, I probably need to give it more time. My last suggestion seems to work a little for me... I lightly lie on a yoga ball to help stretch it. But you don't want to overdo it!!! If you do, it could cause more harm! But I start with the small of my back on the ball and slowly move the ball upward to where the pain is, then if I feel discomfort, I move back to the small of my back. But be careful getting off of the ball, it can be the most painful part. I'd try rolling off the side rather than off the front. When I did this for a couple of days it seemed to help, and I even started to believe the muscle was healing and, stupidly, I stopped! But I will start it up again. Hope this helps.
Yes, I too (a person who hardly ever gets sick, btw) am going through a respiratory illness, going on a week now. I got to coughing so hard, that eventually I had pain on my side and inside when coughing, sneezing, laughing. Now it's gotten so bad that just moving hurts. Problem is I still have to cough sometimes, and it's terrible. I tried 2 Ibuprofen, and that didn't help. I tried the heating pad, and that didn't help either. So, in short, I really have no answer for you. I do feel your pain, however.