Blood in sputum for four weeks, no cough, no fever, no chest pain, have been examined by my doctor said no problem. What do I do?

Blood in sputum. You are already under care of your doctor. Blood in sputum for four weeks should not be ignored. If by now, you do not have a definite answer suggest seeing a pulmonologist. The causes may be gingival bleeding, bronchitis, sinus problems, tuberculosis, cancers, bronchial adenomas to name a few.
Bronchoscopy. Ask for a bronchoscopy. A flexible camera that looks at the inside of your lungs and upper airway. Can be done by a pulmonologist or thoracic surgeon.