Hi Frances! First of all, make sure the tension on your pedals isn't too tight. You can adjust how hard it is to clip in/out.

I used to have a big problem with falling over when stopping because I was leaning the opposite direction from my clipped out foot. So, here's the advice my husband gave me: clip out with one foot, and as you're putting it down, turn your front wheel away from your clipped out foot, i.e. clip out right, make like you're turning left with your wheel. This will cause the weight of your bike to fall toward your clipped out foot. Some folks here do it the opposite way, but this has always worked for me. If you stand straddled over your top tube with your feet on the ground and turn your wheel, you'll see that the weight of your bike naturally shifts the opposite direction.

Anyway, I hope this helps you out some!! It's worked like a charm for me and I haven't fallen once since I started doing it.

Also, they do make pedals that you can clip into on either side. I have those and it's very helpful to me.

Hang in there!