Cotton Swabs and Itchy Ears
A cotton swab (q-tip) can be very dangerous if inserted into the ear canal. There are many accounts of abrasions, wax impaction and even tympanic membrane (ear drum) perforations accidentally being caused by their use.
You are correct in being concerned about using wax removal drops in this case to lubricate the ear canal. Perhaps your physician meant a product such as Eargene, which is over-the-counter ear drops to relieve itching, particularly for hearing aid patients?