OP, for the sake of your family if not for yourself, please schedule an appointment with a practicing psychologist. If you don't get help, you will do something like this again, and chances are that next time you'll lose a lot more than just your job and your family's financial security.

In fact, you have absolutely no reason to believe your former employer hasn't already reported you to the police. They're under no obligation to honor your agreement, nor are the clients who might be accusing them of fraud right now required to respect it. If you are charged, having documentation that you recognized you have a mental health problem on some level and planned to start therapy of your own volition will almost certainly improve your odds of receiving a light sentence.

Your post makes it sound like you're a compulsive thief. People like that don't go out in the morning planning on stealing - many don't even want to steal anything and will feel horribly guilty about doing it - but when they see something of value that they are able to steal, they absolutely cannot resist the urge to do so.