I have a Radeon R9 280, but it won't show up in the options! Instead I just get the shitty NVIDIA GeForce 7900 GS which came with my processor. How can I fix this?
Yep, might be that. Did you connect the monitor to the newly installed graphics card?
In case you did, you might need to configure your motherboard to use the R9 280. It is done in the BIOS. To enter the BIOS configuration press the corresponding key immediately after you turn computer on. The key is different for different models but usually is one of these: Del, F2 or F10. Would help a lot if you can tell what is your motherboard model.
It is also possible that you have both cards active but windows is configured to use the integrated.