The 2 codes were probably 442 and 446 (flow malfunction). Code 448 occurs if the pump siezes, permanent fault and then one should activate the pump with the VST to be sure it's siezed, not just guess. The first 2 codes are caused by the check valve failing and if that's all that's wrong (the pump works and isn't excessively noisy) then I'd just replace the check valve only. Usually once the check valve goes, the pump's not far behind it as it becomes full of water in short order. Apparently you caught yours in time.
I'd advise replacing your check valve now (only), clearing the code(s) and just drive the car not worrying about how, when or why the pump activates because (like I mentioned before), it doesn't always run cold and I think you might be worrying about it un-necessarily as it's probably fine, functioning normally. If after you replace that valve, clear the codes and drive it for a while you don't see the check engine light again, there's no problems.