Can getting a cold block your ears?

Yes. Blocks up your sinuses which are located at various areas in your skull. Particularly they are found surrounding the eustachian tube which connects to the ear. The eustachian tube is how your ear's pressure is maintained. If you have ever been to a different altitude and your ears "pop" or feel stuffy.... you open the eustachian tube (some describe it as yawning) to even the pressure and get your ears back to normal.

yes it can cause a buildup of earwax do to coughing sneezing i had a cold a few weeks ago and it was so bad i had to get the dr to give me wax remover for my hearing