For vestibular dysfunction
I would have thought a Neurologist should be able to test for this, or specifically an Oto-neurologist, your GP/MD would know who to refer you to.
For raised intra-cranial pressure
One way is to have fundus photo’s taken of your eyes, the next time you have them tested at the opticians. Ask them to look for subtle signs of a swollen optic disk.
If you’ve had any MRI’s done, occasionally it shows it up with flattened back of eyes but this isn’t a common finding, so it’s not a reliable test.
Don’t accept a lumbar puncture to test for raised intra-cranial pressure, as it can trigger many more symptoms, see
Plus further info explaining the danger of Lumbar Puncture at:-