I have just downloaded and tried testing my domain with slowloris to see if I could temperarily shut it down with cmd.Whenever I initiate a connection, my internet always slows way down and even stops working but my website never seems to be clogged up. Any thoughts? I know my server is running apache.

Could be due to your ISP. Try it from different box that isn't on a subscriber line.

It doesnt eat bandwidth. It has to be your computer. Slowloris is multi-threaded application and consumes CPU resources and that has to be the cause of the system lag.