My laptop's screen is making a high pitch sound, and it is darker on one side than it is on the other. Does it sound like maybe one of the lights in the back is going out, or could it be something bigger? I just don't want to spend much more money on a computer that I just bought a year and two months ago for $1,300.

Those symptoms can be an issue with the display's power supply inverter. Replacing it requires opening the laptop up. Part replacement cost should be less than $200 (US) depending on laptop model (possibly much less). Suggest you contact the manufacturer or a service center for your laptop and get a quote. It may still be under warranty if you bought it new.