I started a persistent cough starting last night. When I
Need to see a doctor....
I went through your details with diligence. What you describe is persistent cough with blood stained sputum. You also complain of some amount of difficulty to breathe, though not in distress.
Are you running fever?
Do you have chest pain or sweating?
Do you have any known medical condition?
Are you on regular pills?
These are not symptoms of common infection that I would wait it out. I think you should see a doctor at the earliest. A detailed respiratory examination and if necessary a chest X-ray is in order. Treatment will be planned accordingly.
Hope this helps. Let me know if you need clarifications.