Seen a dentist who specializes in jaw pain? Might be you've got a tooth problem or a nerve problem in the nerve that goes around the gums or TMJ or a bite problem, given nothing else has been found.
No idea, but your description of fat around your jaw/neck reminded me of Cushing's disease. Google Images and see if anything looks similar.
If only we could have access to an unlimited amount of funds for acquiring any necessary tests, scans, etc. needed to obtain some answers?? Additionally, the same level of knowledge/information available no matter with which institution the medical specialists obtained their accredited education or the State/area our residence be located in?
At the foundation ≈
[equal human beings▪︎▪︎equal
medical knowledge
opportunities]≈≈
As well, I too have been searching for answers to aid in understanding what is going on with me. Similarly to you, I experience swelling-[what I term being puffy] that comes and can go with some type of link or connection, in part, to~~my period ¤hydration to an extent ¤some relation to do with foods/diet ¤stress ¤activities (specific and amounts.)
My first experiences began with some puffiness that occasionally would appear just in my feet and ankles during my 3rd pregnancy (about mid-way) occasionally. [It was a completely normal, healthy, trouble-free, and full term] At some time following I began noticing, especially in the beginning, that while not pregnant my feet would appear puffy at varying levels with no rhyme or reason to it. Then after some time with continued occurrences I was able to make one small connection that held some influence but was not a specific link to every occurrence: {more than half of the time following me consuming a partial to full soda, puffiness would occur in my feet and ankles; however, the puffiness would occur at times when I had not consumed any soda at all or any other high sodium food or drink}
Around the same time period I made one other small observation not seeming to relate to much of anything that involved consuming soda products:
whenever I had a soda, would take me between 4-6 hours to fully consume, no matter what it seemed like and this had not been the case before in my life (and I really enjoyed my preferred choice of soda!)
As you can see I have made, over time, detailed accounts and observations; this is just my beginning. Since (a couple of decades later) have acquired several other oddities with no obvious connections to very much, anyways. All the while, frequently investing time to researching and reviewing updates to previously obtained information, newly available insights-discoveries-knowledge/information, and reflection over my entire life prior to now.
Any additional insights I have that could be of assistance requires time and space I'm sure this little spot is not quite designed for.