Should I go to the hospital if I've been coughing almost 3 days?

Depends.... If you are also having difficulty breathing, then go to the er. If not, call your doctor as this can likely be treated as an outpatient as long as you are not short of breath.
See a physician. Are you having other symptoms such as fever, difficulty breathing, chest pain? If you have other symtpoms you should see a physician right away. If it is just a cough that is persisting then you should see a physician but it is less urgent.