Thank you for your question. Yes, Q-tips or any other cotton buds are not meant to be inserted into the ear canals as they are too big! You will end up pushing your earwax deeper into the ear canal or may damage the lining of the ear and cause an ear infection. I’ve also seen broken Q-tips lodged in the ear canal or puncturing the eardrum!
It sounds like you may have developed an ear canal infection (also known as otitis externa) and given topical antibiotics by your GP. Usually getting the ear cleaned by an ENT Specialist (by using a mini vacuum suction under microscope guidance) in addition to antibiotic eardrops does help ear canal infections resolve faster. The symptoms do take time to resolve – typically 7-10 days. If you are feeling much better (>50% better after day 3), I would suggest continuing the antibiotics given by your GP. If you are worried or unsure, do get it reviewed by your GP or an ENT Specialist.
Hope this helps.