Hi,
very interested to see your post. I too have been getting neck cracking manipulations from a chiropractor. Although the chiropractor has not cracked my jaw he has done certain manipulations to it - please see post titled "tmd and chiropracty".
In my case the chiropracty on my jaw has not relieved the pain and has actually made the matter far worse. My jaw now feels totally alien to me and my teeth just feel too big and close together for my mouth. This is why I am trying to decide whether the chiropractor has done something that he really shouldn't have.
Also, like you, I now have a muscle in my throat that spasms whenever I swallow. I haven't had to move it back into place yet but you can hear it and if I put my hand on my throat I can feel it - it is a very strong and loud and makes eating or drinking a real drag. Only way of coping with that problem I have found so far is to look sideways when I swallow.
I'm not saying that jaw cracking wouldn't help but if I could go back in time 2 weeks I would instruct my chiropractor to leave my jaw alone. Personally I think in trying to get more movement back into my jaw that he has drastically altered my bite. Whether he did that from the jaw manipulations or whether the neck muscle loossening has done this I am not sure.