Response got long winded. TLDR I'm using this now which was the solution for me: https://www.amazon.com/Audio-Technica-AT2020USB-PLUS-Condenser-Microphone/dp/B00B5ZX9FM/ref=sr_1_1?s=electronics&ie=UTF8&qid=1474319029&sr=1-1&keywords=at2020+usb+plus

My solution was a different microphone. Unfortunately I suspect it won't be the solution in your case. I was using this AKG Pro Audio P3S Dynamic Microphone. After some research I came to the conclusion that Dynamic Microphones aren't really great for recording vocals. At least compared to other types such as Condenser Microphones.

Anyway, before getting my new microphone I tried a cheap Logitech desktop Mic I had in storage (I have no idea why its $40, I got it for ~$8). This was better than the Dynamic Mic but not by much.

So I decided to get a new microphone. I wanted something nice so I started researching condenser microphones. The small issue with them is they usually need a preamp of some kind, as far as I could tell anyway. Good preamps can be $100 bucks and I'm not one to cheap out on hardware so I wasn't going to get a low end one.

Instead I decided on the Audio Technica AT2020 USB Plus. This way the preamp is built into the microphone and everything is converted to digital at the microphone instead of inside the computer, which avoids any interference. This solved my problem with people hearing me in discord.