Well that's what happened the very first time to me. Not after the first line but after a few small ones and then we did a larger one because I guess we were inexperienced and idiots lol. As soon as the drip hit i remember swallowing very often and breathing much harder than usual, and telling myself that it was 'cause it was making my throat numb.
I've only done it a few times and the other times weren't as bad.