girljen,
Congratulations on starting. Trust me, you are over the hardest part. Things will get better. Just keep it up!
since you didn't say anything about your fitness level before you started, I'm assuming you didn't take up cycling to work as something to do in between your marathon running. That being said, it will take some time to develop the leg muscles to cycling. How much time depends on your level of fitness, your willingness to work at it, and your general athleticism. Without knowing you, I can't really say. I can talk about my own experience, and maybe you can deduce from that some meaningful info.
I started cycling for exercise seriously after suffering an ankle injury that prevented me from running. I'd been running 20 to 30 miles a week forever (like 25 years or so) on top of the weekly basketball game, twice weekly volleyball league, and other assorted outdoor activities. I used to be an athlete in college, and still weight the same as I did when I graduated. In short, I was relatively fit and used to exertion.
On the first group ride I got shelled, quickly. I went into the red, eyes got crossed, legs ached and my lungs felt like they were coming out my throat. That was maybe 3 miles in to a 30 mile ride. I kept coming out, each week hanging a little longer, each time going a bit more. I also understood that things improve with practice and began to ride more in between the friendly group rides (sarcasm intended).
After about 6 months I began to catch on. After a year I was solidly with the group. Now five years later I ride as fast, as hard, or as long as I feel like and can hang with any of the local guys. My commute is 6.5 miles round trip. I ride between 120 to 250 miles a week, and have for the last five years. Clearly my fitness level doesn't come from riding three miles to work. Yours won't either.
I suggest you pick out several routes that add some daily miles to your riding. Vary them so you don't get bored, match what you do with how you feel (feel tired, go slow and rest, legs hurt from yesterday's effort, go straight home) so that you don't prevent yourself from doing tomorrow's ride. Keep putting in some effort and I promise it will get easier.
Best wishes, and congrats again for riding to work.