I’m assuming the side venting would be over the walkway or other area that is not approved by code. Are you saying that side wall venting of high efficiency furnace and power vented water heater is not permitted in Chicago in general? There are several restrictions but I’ve never heard that it is forbidden.
You can try opening the wall / ceiling wherever it is necessary and try to enlarge the holes around the PVC vent. If this is not possible you’d have to reroute the vent pipe to some approved location. The noise will most likely not go away otherwise.
Just do some damage assessment and pick the least complicated way. It’s difficult to suggest anything without knowing the layout of your installation.
Please let me know if you have more questions but describe in detail the location and why do you think that you cannot vent through the side wall. How about the rear wall of this building?