Congrats! I started running a little over a year ago. I now regularly run 5k races because they're fun, and although I can run the whole 3.1 miles without stopping, I am very slow! (It's not uncommon for little kids and speed walkers to finish before me, lol.) But, it's still a great feeling.
And while walking has just as many benefits and is a little easier on your body, as mentioned above, I usually choose to run when I go out to the trail for exercise. Because I can.
Keep up the great work. Keep a running journal, so you can look back to see your progress.