Hi Wendy,
I'm quite new to this myself but I'll throw in my 2 cents worth. I started commuting to work about 3 weeks ago and it really helped that a co-worker of mine lives close to me and also bikes into work. If you have a friend or significant other that can go on little rides with you, it really helps.
I don't know how fast you are spinning, but if you have your bike in too high of a gear you are going to wear yourself out faster because you are pushing your legs so hard. Try a lower gear. It may feel like you are working harder because you are spinning faster, but it is easier on the legs. Experiment with the gears. Also make sure that your seat is at the proper height.
You are doing great. Your fitness will improve and you will be driving everywhere in no time!
Maggie