Lower back pain after coughing

I had a cold about 10 days ago and had a 30 min spell of really bad coughing. On one of those coughs I was bent forward and I got a sudden very sharp pain in the middle of my lower back that almost brought me to my knees. After that any coughing or sneeze has been excruciating and if I would bend it would "catch" and be very bad pain. After a couple of days I went to the orthopedic walk in clinic and they took and x-ray, said it was likely just a pulled muscle. They gave me a 5 day steroid pack and sent me on my way. If I just sat or walked upright and didn't cough or sneeze, I had no pain. I have no numbness or tingling.

It is now 8 days later and the cold is long gone. But my lower back pain is still pretty bad. It has changed from something that is no pain that suddenly causes intense pain if I move or bend the wrong way, to a dull ache and stiffness. The pain has also a bit more on my right side now. I guess what concerns me is that it doesn't really seem to be improving at all. I have progressed from using ice to using heat. I am a heart patient so it isn't a good idea to take NSAIDs. I get in the floor and do some knee to chest stretches and also I am able to do glute bridges (neither cause pain or discomfort). If I do supine knee side to side, it really will hurt when I try to move my knees back to center from the left side, so I do not do those. If I sit and roll my spine forward, it will cause mild pain in the lower lumbar region, as does arching my back. Does this still sound like a pulled muscle? Are there any good stretches I should try? I am just surprised that I'm not really seeing any improvement 10 days after the injury.

Thank you for any suggestions.