Engine made some noises today that sounded like a bad water pump

What engine size? What kind of noise? Can't tell much over a computer unless you give details.

Water pumps make lots of different sounds. If it sounds like a rough, grinding noise, serpentine belt idler pulleys will make that noise too. The noise can go away once the grease softens and starts to lubricate the bearing. Bearings can make a buzzing noise when they develop wear at higher mileages. At first that will also go away, often a few seconds after starting the engine. As the wear gets worse, the noise will take longer to go away, if it does at all.

Spring-loaded automatic belt tensioners can become tight on their pivot and fail to hold proper tension on the belt. That results in a chirping or squealing sound. To identify that, dribble a little water onto the smooth back side of the belt while the engine is idling. If the sound changes, check the operation of the tensioner and for proper pulley alignment. With the engine off, tug on the belt and release it. You should see the tensioner pulley move, then move back to tighten the belt. If it sticks and leaves the belt loose, replace it and the belt.

Often a noisy item can be found while listening with a stethoscope. You can also remove the belt, then start the engine. If the noise is still there, it obviously isn't belt or pulley related. That would point to something inside the engine.