Do Prednisone And Doxycycline Interfere With Each Other?

Greetings, I have just begun prednisone and doxycycline and would like to take Nyquil Severe to deal with my cough tonight. I have checked to see if any of the active ingredients (acetomenophen, dextromethorphan, doxylamine succinate, or phenylephrine) interact in a problematic way and have seen nothing on line but would like an informed medical opinion. Thank you.