Yes, those numbers are high, and as you suspect, the voltage regulator is probably failing. That regulator, however, is integrated into the alternator itself. I would imagine that you can replace just the regulator, but I don’t know where you’d get one. Even if you did manage to track one down, you’ll still have to pull the alternator off the car to get the regulator out of it, so you may as well just put an alternator on it and save yourself the hassle of disassembling the alternator.
The voltage on a battery that’s been sitting long enough for the dark current to stabilize should be around 12.4 volts with a full charge. When the car is running at idle with no load on the alternator, the voltage measured at the battery should be between 13.2 and 14.4 volts. Any less than 13.2 and the alternator isn’t producing enough voltage, and much about 14.4 and you’ll start boiling the electrolyte out of the battery. The battery light on the dash is only looking for a low voltage situation, not a high voltage one.
On a completely unrelated note, something else to keep in mind, that you may want to check on the next time you work on that Cavalier is a ground cable that’s attached to the bell housing of the transaxle. With the engine running, measure voltage between that cable on the bell housing to the negative terminal of the battery. Anything more than 0.1 volts is cause for replacement of that cable. It’s attached to a lug under the battery tray and it tends to corrode there. Chassis ground problems can cause all sorts of strange problems that become an absolute bear to track down, but like I said, that’s unrelated to your current concern.
Also, I don’t know if you know what I mean by dark current, so I’ll explain. Dark current is the term referring to any drain on the battery that occurs when the car is off. Things like the clock, the radio memory, the theft deterrent system (if equipped) are all examples of dark current.