While there are excellent ways to remove earwax (cerumen, as doctors
call it) from the ear canal, I am doubtful that your complaint is due to impacted cerumen in your external auditory canal. Usually, when people have an upper respiratory tract infection, the entire upper part of your airway, including your ears, will have some inflammation and increased mucous production. Because your inner ears are lined with the same mucous secreting cells as the rest of your upper airway, this mucous will need to be able to drain from your ears to the back of your throat, which occurs via the eustachian tube.
This tube is a thin structure that is also important because it allows for pressure to equalize between the outside world and your inner ear (as when your ear pops as you go up an escalator). When this tube is inflamed, the diameter of the tube decreases, the smooth muscle lining spasms, and the tube doesn't function properly (eustachian tube dysfunction). This makes it impossible for fluid to drain, and, more importantly, for the pressure to equalize, which leads to the feeling you are describing. Usually, it will resolve by itself or with over the counter cold remedies, but please speak to your doctor as needed. There are over the counter drops that will help with ears wax if you want to try those, too.