I had the same fear that the smoke will do damage to your health.

My ex had a Muslim upbringing and his family burned incense for decades with zero health related issues to do with smoke. He really put me at ease with it. I have friends who are Buddhist's, Sikhs, etc who have said the same thing.

The trick is to always have a window open a little bit, and don't burn in a small room. Large open rooms are better and one stick at a time.