Hello I had this, swishing in ears, strong pressure in my head and could not lay on my stomach the pressure was too much, and I had bad headaches and just feeling pretty rough, it turned out to be IIH which is Idiopathic intercranial hypertension, the fluid in my spine was making too much and increasing pressure in my head, make sure your talk to your doctor if you think iy could be, not a lot of people know about this illness, I had to have a lumbar puncture to check the pressure in my head and it was very high, hope this helps
So, that swooshing is a sign of inner ear issues especially the Eustachian tube. Do they have the ear nose and throat specialty of doctors in your area? I would think an ear nose and throat doctor or ENT would be great to help you solve this situation. Hold your nose and blow, your ears will pop. This is called a reverse ear pop and if you do it several times, it can help clear your ear (my ENT taught me this.).
This is probably much more to do with your ears and the inner tubes. Do you hear a swishing sound too? Is it more on one side than the other?