Both my kids took singulair when they had bronchitis. Similar to you I had my reservations and raised it with my pd. End result I gave it to my kids because their recovery was my priority (she didn't give me any other alternative drugs instead she told me the side effects if I didn't give).
If you're uncomfortable with feeding a medicine maybe you can seek 2nd opinion or TCM.
As for my case my boys recovered and I didn't see any side effects.
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