An excellent suggestion. If your Civic has an automatic tranny, the radiator you replaced might have been allowing the coolant and the tranny fluid to mix. While replacing the radiator should eliminate that problem, you may also want to flush and refill the tranny once you get the engine cooling system fixed. In '98 Civics with automatic trannys, both the engine coolant AND the tranny fluid (which is used as a coolant for the tranny) run through separate sections of the radiator… and these can form leaks between the sections. These leaks will allow mixing, and adversely affect the engine coolant’s abilities and absolutely destroy the tranny.
Hopefully it’s just the air remaining in the cooling system that’s causing the current overheating. The way I air bleed my Corolla, I drive the front wheels up on ramps so the top of the radiator is the top point in the cooling system, remove the radiator cap, turn the heater control to max heat, and idle the engine until water starts to pour into the top of the radiator. I can peak through the radiator cap hole and see when the water starts coming in form the top hose. Takes 5-15 minutes. Sometimes I completely remove the top radiator hose from the radiator & direct it to a bucket, so when the water starts pouring out I can judge how fast, as that gives me a way to judge the thermostat and water pump function. When you do all this don’t walk away, keep an eye on the radiator fill level at all times, and be ready to pour more coolant mix in, as the level can drop really fast.
Most auto parts stores stock this as a diy’er test kit.
Note: I get the sense you are assuming this problem isn’t due to a faulty water pump. Before going too far down other paths, suggest you test that assumption. Faulty water pumps – usually it is worn off impellers – causing overheating is a pretty common thing reported here. Best of luck.