No data was given of the exact location of back pain (upper or lower back pain).
If it is upper back pain, then it might be related to spasms of the diaphragm because of the coughing itself. Treating the cold might stop the coughing and back pain.
If it is lower back pain (waist), then during coughing the spasm of the diaphragm might increase the pressure in the abdominal cavity where the organs are already situated in reduced space. So, something might be putting extra pressure on the spinal nerves in the area. This kind of pain should not last longer then several minutes after the coughing.
However, if it lasts longer, then some more serious health issues related with the pregnancy might be occurring and you might want to visit Emergency service or your gynecologist as soon as possible.
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