After commuting, I always shower before work. My first time commuting, I loaded up the bag with all my necessities and boy did it get heavy half way though the 16 mile commute. We have a nice locker room that we are allowed to keep locks on overnight, so I keep all my necessities there now. What about keeping everything at your desk? Do you have a drawer you can store it in? It's sort of a pain to go to your desk, then the locker room, but it's much easier than hauling the blow dryer to and from work every day.

Also, I find I am unable to bike every day. So I load up on the days I drive with the clothes I'll need for the days I commute and keep them in my locker. Maybe if you have an empty drawer at your desk, you can do this. Your commute is pretty short though, so if you can't keep things at work, carrying it shouldn't be too bad. Try to plan the lighter clothes to wear on days of your commute, so it's lighter on your back. Also, if you can keep an extra pair of shoes under your desk, that could save some weight.

Good luck and enjoy your commute!!