For a wax blockage the normal procedure to remove it is to take a large syringe and inject warm water into the ear canal to loosen and remove the buildup.
The syringe has no needle on the end, instead it has a tapered stainless steel tip. To obtain something similar check a veterinary/agricultural supply store and ask for a large plastic syringe the type used to give medicine to livestock orally.
A sinus/inner ear infection is also possible, the only remedy for this is to have a doctor look into the canals and check for redness and inflammation and prescribe the necessary antibiotic.
Placing a Q-tip into the ear canal can compact the blockage further into the canal and is not recommended, If you have any loss of balance/ headaches or soreness see your doctor immediately.
Permanent loss of hearing can result if you don't get this taken care of right away.