The liver cleanse is also based on Epsom Salts . With the diet you have been eating (if this has been long term) there is in my opinion no real need for a liver flush.
In my opinion you need to stop taking all things which contain laxatives, period. Otherwise you will not get out of this viscious circle. It sounds to me like you need a naturopath or similar person to help you through this, as it is quite clear that you are very frightened and anxious.
A lot of problems with the digestive system get enhanced by feelings of fear, so I would suggest you start manifesting that you let go of your fear of having problems with bowel movement and you let go of the dependence on laxatives. If you also start manifesting that you have regular bowel movements and you let go of the physical and psychological need for laxatives you will help your body along.
Most of the time problems like these are both physical and emotional, so you need to resolve both before you get better.