I have persistent cough for 1 month now. my dr prescribed doxycycline. is this right antibiotic for my cough?

It depends.: It depends on the cause of the cough. If it is viral bronchitis, an antibiotic won't help. If it is tuberculosis, it won't work. If it is heart disease or gastrointestinal reflux, it won't help. If it is sinusitis, it might help.

If..: If the cough is caused by a bacterial infection doxycycline can work very well. However if it is caused by other problems like allergies, acid reflux, a resistant bacteria to that certain antibiotic it might not work. It all depends on the whole picture of your ailment. If they prescribed it to you most likely they found a reasonable evidence in your examination to suggest a bacterial infection.

Cough: Yes, it seems appropriate. Chronic coughs can be caused by atypical organisms like chlamydia penumoniae and mycoplasma both of which respond to doxycycline. On doxycycline you can't take it with milk and should best take it 1 hour before or 2 hour after meals with water so it does not get stuck in your esophagus. Also use hats, sunscreen, and sunglasses as it sensitizes you to the sun.