Can you list your router brand and model number? Does your PC (Ethernet) plug into the same router that is suppling the WiFi or do you have multiple boxes?
My guess is that there is some kind of QoS (Quality of Service) algorithm running on your router. Generally, if one device tries to upload a bunch of data it will swamp the connection and make using the internet painfully slow for other devices. To combat this, routers will sometimes have a bandwidth limiting or priority based QoS running. It's kind of like everyone gets one small piece of cake rather than someone grabbing the whole cake. The issue is that with your desire to twitch stream, you want a bigger piece of cake. Depending on your router/setup, you might be able to give your PC more priority or more bandwidth. You can look for QoS setting on the router configuration page. Also look for WMM in the wireless part of the setup. With the router information I can advise you better.
As an afterthought ... there is also software out there that runs on the PC in an attempt to accomplish the same thing. Are you running Killer Network Manager software or Asrock XFast Lan or anything like that?