Simply put, my alternator is charging at right around 16 volts. Could this effect the performance of my car? I read somewhere it should charge between 12.8 and 14.8 volts
It should charge around 15 volts. I've heard as high as 15.8 volts but I think in the low 15s is normal. Once you get up toward 16 volts or more you run the risk of frying lots of electronic components. Ask me how fun that is to fix.
It sounds like your alternator's voltage regulator isn't working properly.
Get it checked for free at the local auto parts store.
Same thing happened to me a while back. Voltage regulator slowly went over time and i didn't realize until it suddenly started spiking to 20 volts and blew out most of my bulbs
If you're an electrical engineer type, you might be able to replace the voltage regulator. For the rest of us mortals, we get new alternators when those go bad.