unlikely a type 3 on an opposing side from contracting muscles, but, its very common to cough so hard that your diaphragm muscles contracting and the force of your cough have mis-aligned facet joints on one or both sides of your spine.
its painful, which can cause extreme muscle tightness and pain in attached parspinal muscles.. not likely a tear in your back.
coughing could, however, cause tears in oblique, and abdominal muscles.
Rest, ice, anti inflams if your stomach tolerates, and go see someone when you get a chance.
feel/get better DP....we got a ride heading our way in the morning.
