Yes it can. It can also make you feel like you have a tooth/jaw ache even though you don't. Can also make the side of your face feel numb and "Squishy". It is wax, but also bacteria that can turn into an ear infection if left alone and not cleaned/removed.
Hopefully they gave you an ear lavage (Flushed your ear canals) if it was necessary. If not, you can get some over the counter drops that will break up/loosen and remove wax from your ear canal. Just follow the directions on the bottle. Be careful if/when you use Q-tips. Do not go deep into your ear with them pushing more and more wax causing it to compact. Use them only around your outer ear areas.
Every few months, I use a water-pik (The kind you would use for your teeth) to clean my ear canals out with because I have the same problem, and they start hurting. I use low pressure, warm water and a dash of peroxide in the basin. Gross, but big chunks come out and instantly feel better. This is pretty much the same as an ear lavage, they just use a syringe and force saline/water into your canal, and it all comes out into a small bowl.
Hope this helps, and get the drops or try what I said above.