Your marriage by a JP is recognized as a Civil, but not Sacramental Marriage. The Church considers a valid Saramental Marriage as indissolvible. Based on what you have written here, what you should visit your local parish, and explain the situation you are in. Once you understand why the Church encourages and legislates that we should marry in the Church, you will simply need to do is go to confession, confess that you attempted Marriage at a JP, and, after you have received absolution, with the resolve to live a good Catholic life, you can receive communion again.
Simply put, if you are sorry for breaking the legislation of the Church regarding Marriage, and go to confession, you can recieve communion. But it is best to speak to your local parish priest first, so you can understand more fully what the Church teaches and practices regarding Marriage.