What OS are you using?
YOU are funnny! I love statements like this:
I want to be able to input the URL of my computer and immediately see my webcam.
Ok, so go ahead and turn on IIS! You do have IIS enabled right? IIS will allow your station to become a website. Now, point that IIS controller to a virtual directory, that is running a java app server, that is connected to the webcam! It really is that simple!
BTW, you will need a NAT, and a firewall! NAT is for the INTERNAL network translation. In other words, the fixed IP on you computer is OUTWARD facing, but your PC really has an unroutable IP address, and the internet will not know what to do with that IP address once you have placed it into a browser that is on the internet. The NAT will translate your 22.214.171.124 address into a address like 192.168.1.1.
Or, get a third party app. Or get a a webcam with DVR, and publish it! The WEbcam DVR is SO SIMPLE to deploy, just takes capital cost for hardware.