An interesting question because I have just had to make an appointment to have my itchy ears investigated by my surgery.
I was informed after investigation that in one ear I had developed eczema and in the other bits of skin had blocked my inner ear which caused the itching. Of course a wax blockage can also cause itching and partial hearing loss.
In my case the ear I had eczema in was clear of wax but my other with the skin had to be syringed to remove the skin. Once done I could hear in that ear normally, however I am profoundly deaf in the other.
The nurse who syringed my ear suggested I insert 3 drops of extra virgin olive oil in my itchy ear which will help it to remain moist and hopefully stop the itching. These drops can be purchased in a pharmacy.
May I suggest you have your ears checked for wax and/or eczema and syringed if necessary.
If after investigating your problem persist you should make sure your doctor investigates the reason for the problem thoroughly.
I know the itchiness in your ears like mine is probably driving you mad, but whatever you do please don’t be tempted to put sharp implements in your ears to try to stop the itching.
Good luck