I agree with those who say not to lie flat on your back. Have you been checked for GERD?
And
I have a totally different suggestion - don't use your NeilMed at night. Here is my logic - when you rinse your sinuses, you activate mucus production. That slides down the back of your throat, causing a tickle, and setting up the cough reflex. And the entire cough cycle. When that happens to me, my only choice is to sip water, take deep breaths and sleep in my recliner - the same as my husband does when his GERD acts up.

What I do is, around 8pm (I go to bed at 11), I stand & bend forward from the waist then stand, reaching my arms up & breathing deeply -I do it several times, then do one or two Aerobika breaths (similar to Acapella) then huff cough - for me, this brings mucus & sputum from both lungs and sinuses. Usually once is enough, but sometimes I need to repeat. Oh, and I also avoid using any inhalers near bedtime - again the "tickle factor"

Sue