I've been feeling more tired and have some cough and fever. When should I see the doctor?

Depends. Typical viral infections last 7-10 days and slowly improve over time, but if you symptoms include shortness of breath, chest pain, coughing of blood you should see a doctor immediately.
Breathing problems. If you are experiencing cough associated with significant fever, you may very well have pneumonia, and that will require an antibiotic. Most lung inflammations are associated with fatigue, but this is a nonspecific symptom. Other potential causes include a blot clot in the lung, tumor, and other inflammatory conditions of the lung. So, yes, it could be something bad. Best to have it checked out.