You could have some fluid on your lungs. When you lie down, the fluid spreads out into a shallow pool and covers the maximum amount of alveoli. Then you need to cough so you can breath. A week after valve surgery, this situation is not uncommon.
You can pile a bunch of pillows at the head of your bed, so that you can sleep with your head and chest higher. Or you can sleep in a recliner, if you happen to have one of those. You should also follow up with your surgeon about this. He may want to do a chest x-ray. He also may want you to be doing breathing exercises. In fact, if you still have the spirometer that you were presumably given in the hospital, I would recommend you continue using it until directed otherwise.
If the coughing is getting worse instead of better, it becomes an urgent matter to get medical help. If you develop fever, I would regard that as a medical emergency. But unless the coughing is getting much better day by day, I would call the doctor's office tomorrow.
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