I don’t think the problem is the new radiator. That wouldn’t be my first guess. I’m assumng you have no newly developed engine problems you’ve noticed and no trouble codes (check engine light) flashing and the only thing you’ve done recently is replace the radiator with a new one and the coolant level is to spec and the mixture is 50/50 and there are no coolant leaks.
After checking the fans and assuming you find them working correctly, I’d probably take out the thermostat and test it in a pot of hot water to make sure it is opening fully and at the right temperature. Then I’d read up on the cooling system bleeding procedure recommended by the manufacturer and do that step by step. If that didn’t fix it, I’d come back here and ask what to do next.
One tip: If you find yourself stuck in traffic and it starts to heat up and you need to somehow stop it from overheating to the extreme, one thing you can do to help cool the engine is to turn off the AC and turn on the passenger compartment heater to max and the heater blower to max. It will be uncomfortable so roll down the windows, but it might just cool the engine enough to save you from a head job.
A couple years ago I replaced the radiator in an early 90’s Corolla and the third-party-non-Toyota-brand radiator I bought (new, for less than $100) from the parts store didn’t have nearly as many cooling fins on it as the original. I live in a mild climage where it rarely gets above 95 deg and it doesn’t have air conditioning and it has a manual xmission. So even with fewer radiator fins, it still cools the car fine. That’s why I don’t think the radiator is the likely problem on your car.
If you think it is the radiator, if you still have the old one, it is quite possible a local radiator shop could fix it for a reasonable price, considerably less than a new radiator from the dealer.