Shake programs were originally designed for obese and morbidly obese people to lose a lot of weight quickly at the start of their weight loss journey. They were designed to be used under medical supervision, and really that is the way they should be used. The initial fast weight loss was to reduce any medical problems obesity was causing, and to give incentive to continue the weight loss journey by using food and exercise. Unfortunately now they are marketed as the quick fix for everyone's weight loss when they really aren't meant to help with those last few kilos people struggle with.
Given your height and weight you're already close to your healthy weight. Shakes probably won't be the answer. If you want to try it by all means do, but talk to your doctor first. Very Low Calorie diets really do need to be done under medical supervision as they subject your body to starvation conditions.
Have you tried keeping a food diary? The site that Jewles mentioned, Calorie King
, enables you to keep track of what you eat and how many calories it's worth. There are two possibilities why you're not losing weight. Either you're still eating too many calories, either by picking the wrong healthy food, through too much snacking (even healthy foods add up!) or through excessive portion sizes. Or you are eating too few calories. If you are cutting down what you're eating and excercising too much then your calorie deficit may actually take you into starvation mode. For instance, if you're eating 1300 calories per day but exercising away 500 calories then that only leaves your body 800 calories to operate. By keeping a food diary for a week or so you should be able to see where the problem is.
Here is an article about weight loss plateaus that may help: Plateau Busters