Believe it or not I had exactly same problem back in the day, and I used to smoke cigarettes then, which is why I asked if you were a smoker.
I had these nagging sensations in the throat, surprisingly they were somewhat pleasant, as in I actually enjoyed what felt like warmth and movement in my throat. But sometimes they were getting slightly too strong and it worried me. It all started as my self-awareness increased as a result of my Buddhist practice. I did not meditate back then but did apply serious effort to practice mindfulness.
Around the same period of time I felt increasing disgust to the smell and taste of tobacco products. As my self-awareness grew, I kept enjoying the sensations in my throat but did not want to experience the smell and taste in my mouth. Also, my head started spinning a bit too much after having another cigarette. So at some point I started to reduce the frequency and amount I smoked, until I quit. I never applied any force, never used nicotine patches - it just happened by itself, through awareness and disgust and some head spinning. As I quit smoking, the throat sensations have briefly increased, and then were gone forever.
I'm not saying your case is the same, but perhaps it's not entirely out of question that your awareness of your body has increased as a result of your meditation practice, and now you feel what was always there but you simply did not notice before. In a way, this could be interpreted as your throat talking to you: "please stop smoking". Might as well listen :)