Did your ENT run any tests on you -- tilt table test, caloric test, etc.? If not, maybe start with that. If he did, see if you can find a place around where you live that does "vestibular therapy". They can test for additional balance disorders with the auditory nerve, brain, eyes, etc. Certainly vertigo can cause the symptoms you mentioned & it is not always because of a problem in the ears (regardless of what your ENT may tell you).
If that's the case, the solution is just some simple exercises that you can do mostly at home.
Head pressure isn't a "major symptom" for Chiari is it? From the reading I have done on it, it seems to be that "chronic migraine headaches" or "head pain" are the most common pattern in Arnold-Chiari. What do you know about