Hi & welcome!
Sadly you’re not the only one who’s been gaslit, ignored, dismissed etc about your symptoms, but I’m glad that you’ve been able to do your own research and to find out a diagnosis for yourself!
Your symptoms of swallowing difficulty, strangulating feeling, things getting stuck are classic ES symptoms, numbness & tingling indicate maybe the trigeminal nerve or facial nerve being compressed. Pain in the base of skull is common, it could potentially be the occipital nerve being compressed by tight muscles, or maybe from the styloids? The vagus nerve can be compressed, I’m not sure if that could cause the heat intolerance etc. The styloids shouldn’t affect the legs, but other members have found strange symptoms in the lower back & below…
Obviously we’re not doctors, but looking at your scans there’s clear compression of the IJV on your left side between the styloid and the C1 process. Also on the right, it looks as though the left is maybe the dominant, larger IJV so compression of that would have more of an impact. The styloids are longer than average, quite wide at the top, & both quite pointy at the bottom end so all those factors can cause symptoms. Your left side looks like there could be a bit of calcification on the stylo-hyoid ligament making it longer, although whether it’s that or a long styloid doesn’t matter… The hyoid bone can’t be seen very clearly, but in the image of your right side it does look as if it could be quite close to blood vessels so could cause symptoms- the strangulating feeling is often seen with hyoid bone syndrome or calcifications on the lower end of the stylo-hyoid ligament. I can’t see enough of your neck to judge whether you have military neck- a loss of the normal curve of the neck- it looks a little straight on image 3523 but that could be the angle it’s taken…
As for what to do next, that’s a tricky one! Obviously the NHS waiting times are long- are you able to afford private consultations or treatment? I did go through the best UK doctors in @Blodyn 's post, here’s a link:
But certainly I think you’re on the right track with ES!