I would recommend that you go to see your primary care doctor
about this issue. There are a few different things that can cause persistent itching of the ears, and your doctor can look inside your ears to help figure out which it might be.
You are also right that you should generally not stick any objects into your ear canals, as this can lead to trauma to the ear canal and doesn't usually solve the problem of itchiness in any event.
One of the most common causes of ear itching is a buildup of wax inside the ear canal. In addition to itchiness, it may also cause a sensation of dullness or trouble hearing. If your doctor finds a large amount of wax in the ear, they can clean it out for you or prescribe wax softening drops to help keep the canals clear.
Another common cause of ear itching is otitis externa, which is an infection of the ear canal by bacteria. This often causes drainage of material from the ear, in addition to itching, and it can usually be effectively treated with prescription ear drops.
Start by seeing your primary care doctor at your earliest possible convenience.