Is it fine to go the gym while having cough?i only take the cough syrup before sleeping.

Depends: well it actually depends on the reason of the cough,you need to get checked by a doctor if the cough is present for more than 2 weeks and doesn't get better.

It all depends : on what is causing the cough, is it constant, persistent , annoying etc? If you know your cough is not infectious and not disrupting , you may go to the gym. Do be considerate of others.