Is it dangerous that I have a strange feeling in my throat?

Without examination, it is impossible to assess what may be the cause of a strange feeling in the throat and whether it is dangerous. You are taking an analgesic and anti-inflammatory drug - so I suppose that there is some condition that requires such a drug. Perhaps it has something to do with throat ailments, but there is too little information to say anything more. As for the naproxen drug itself, contact with a doctor is required if symptoms of hypersensitivity reactions occur, such as difficulty breathing, wheezing, tightness in the chest, swelling of the eyelids, face, mouth, throat or tongue, rash or itching. However, I do not find information that the preparation can cause the growth of polyps. I enclose additional information about Apo-Napro (I think that this is the drug you use, because Apo-Naproxen is not available) - prescription preparations can be reserved at GdziePoLek and collected stationary upon presentation of the prescription: https://www.gdziepolek.pl/produkty/6067/apo-napro-tabletki/apteki/w-warszawie