Severe itchy tonsil when I've got a cold?

I'm 41 and this happens to me nearly every time I get a head cold. If I've been lying down at night or otherwise, the drainage must trickle down my throat, which causes me to cough a little bit. However, once in a while, one of my tonsils (and they are quite big) feels like it's being tickled with a feather. I try to keep calm but whenever I swallow, it gets worse, causing my eyes and nose to run and I have to cough to the point of gagging. The episode lasts for a good 15 minutes until it calms down again - usually a cough drop or something else helps. I was just wondering what this is all about. I understand that drainage can cause tickles, etc. but these episodes are quite intense, painful, and just wear me out. I do take medications for the congestion or sinus issue, whatever is bothering me. Having my tonsils taken out is out of the question - no insurance. Any ideas?