When you say "usb port that has plugs for headphones and microphone" do you mean a small USB soundcard for your Mac? Something like this for example:
http://www.amazon.co.uk/3-5mm-Microphone-Earphone-Adapter-Laptop/dp/B00C92Z2XC ?
Could you clarify some more on your exact set up please? We are not sure why you require a mixer with the use of such a soundcard but this really depends on what type of microphone that you have? Is it a 3.5mm jack or 1/4 inch jack or XLR connection? If its a 3.5mm jack then you can go straight into such a soundcard with the microphone without the need for a mixer?
But it does sound like you are just picking up lots of background noise as you just have the mic level up quite high basically. What type of microphone is it? Dynamic / Cardioid or Condenser? Certain microphones will pick up background noise more than others due to their pickup patterns / directions. If the microphone is omnidirectional it is going to pick up noise from all directions at an equal level.
By turning up the mic level quite high on the mixer you are just boosting the level of the background noise. Try perhaps speaking into the mic much closer or louder so you do not need to turn it up louder to compensate for low levels. It might even be worth investing in a mic shield to prevent it from picking up some of the background noise. Also make sure there is nothing in your room that is particularly causing the noise. Try the mic in different positions and away from any such things. There is likely several factors that could be causing this.
Also, what stream encoding software are you using? Its possible that the software or perhaps even your soundcard has some noise reduction settings, we are pretty sure actually that Mac's have one built into the 'Sound Preferences'. This can help filter out some of the noise.
We hope that this helps.