Hello, Usually severe exertion can cause displacement of the IUD, but, cough alone causing this is a rare possibility. As you cannot find the strings and you experience abdominal pain with every activity, it is apparent that the coil has been displaced. You need immediate attention from a specialist to locate the coil and see what can be done to recover the Mirena. You would need a trans-vaginal sonogram and an abdominal MRI to see where the IUD has gone to plan further management. Please abstain from intercourse until you get proper treatment. Hope this helps.