Blood in sputum. Are required for that?

I have been diagnosed with infection in right lower chest in x-ray 15 days back. Prior to that I had a dry cough for 4-5 weeks I found blood in salaiva in the morning. Doctor prescribed me some antibiotics and after that I have not noticed blood in sputum for a few days. But from last 3-4 days again I can see some blood in my salaiva after I cough. There is no mucus coming up when I cough. After coughing up the Color of the salaiva is redish. Generally I don't cough up much in the day. I have dry coughs for 4-5 times in a day. The mucus is stick in my throat I often need to clear it up. Do I need to do any other tests or any other medicines are required for that? And please let me know how long it takes to heal from the chest infection. I am really worried if it is because of some serious issue.