The light we see from the edge of our universe was emitted almost 14 billion years ago. I don't think the universe had a radius of almost 14 billion light years back when the light was emitted.

This is why we usually talk about the observable universe. This one has a radius of 14 billions light years. We however do not know what lies beyond it.

Do you know if there is a simple equation that clarifies the relationship between the age of the light and the distance it traveled in an expanding universe, maybe something like this?

You may want to read about 'comoving distances' Does it help?