I’m so sorry that you have such extreme symptoms from the potential ES, & the POTS & CCI! I did start to feel pretty ill myself from ES & IJV compression, with the off-balance feeling, head & ear pressure, brain fog etc. but nowhere near as bad as your symptoms are…
I’m really glad you’re able to see Mr Axon privately, as @jimjammer123 said, he is an expert with pulsatile tinnitus & has done lots of research into this, so definitely mention this symptom to him. He did both my surgeries; I did have pulsatile tinnitus although it didn’t irritate me too much, I mentioned this by chance at my first appointment & he got very interested then! He will say what scans he wants you to have done, & generally likes them done in a certain way, so leave that to him; a CT with contrast will probably be needed though.
With your symptoms, VES can definitely cause IH, & quite a few of your symptoms could be due to that; I presume you’ve had a read up of that? If not whooshers.com is quite a helpful site… The vagus nerve is commonly affected by the styloids, so can cause digestive issues, and possibly breathing issues. And burning mouth is quite a common symptom with ES, as well as sore throats. The spinal accessory nerve can also be affected which can cause shoulder pain, & also arm weakness. There’s deeper info about which nerves can be affected in the Newbies Guide Section 
ES Information: Common Symptoms And Possible Explanations For Them - Welcome / Newbies Guide to Eagle Syndrome - Living with Eagle
@jimjammer123 's idea about the rush of fluid in your ear could be right, my first thought was that it could otherwise have been a nerve sensation, as some members have found that their ears feel wet (but aren’t) or like they have cold water in their ear, which could be the glossopharyngeal nerve. If it was a CSF leak, quite a few members have had these, & sometimes get clear fluid drain from their noses, the high pressure can cause a leak & some people cycle between high pressure, CSF leaks & then low pressure before it builds again…
There have been a few discussions about the best places in the UK for CCI you could have a read about, I don’t know too much about this…
The styloids can sometimes be seen on a panoramic x-ray, yes, but they’re not always clear, & wouldn’t show VES at all. As this would be more radiation I wouldn’t worry about having this done… I think other members have had venous sinus stenosis & VES too.
After my first surgery I did feel loads better, & the worst of the vascular symptoms went away, although my situation wasn’t as complicated as yours! Mr Axon is an excellent surgeon though…
I think that’s most of your questions answered! I hope you’re able to read up a bit without aggravating your head pressure 
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