@ThatVeryQuinn do you warm up before you try singing the higher register songs? I find myself in a similar situation, and I'm not sure if it's a coated throat I keep clearing, or vocal discipline I haven't learned. Warming up with a song or two helps me. Not you?
@Filene I have a problem when it comes to coughing in general, but I'll try warming up a bit more once in a while and see if that affects it.
Actually, now that I'm trying it it seems I can hit a higher register than before after getting things cleared with a lower register song.