Amyjade-
First, congratulations on your start and commitment to get healthier!
You're going to love how you feel!
Now, on to the calf problem: You said that you stretch before you run. That's OK, but not really effective in actually stretching your muscles. Your muscles have to be warm before you stretch. (That's why stretching
after your workout is way more important than before.)
You indicate that you are already doing a walk/run combination so try this: Walk at a moderate pace for 10 minutes (or less) just until your muscles warm up, stop and do 3-4 calf stretches, then run a short distance, stretch, walk, stretch, and so on. Incorporating stretching into your workout while your muscles are warm should help this problem. I agree with MBN, if your calves tighten up don't just keep trying to pound through it. You'll only get injured. Remember, exercise is something that you have to practice. Start slow, warm up, stretch a lot, and you'll be cruising along in no time!