I think you're miscalculating your calories. Given what you've described eating, there's no way you're only eating 550-600 calories a day (and if you are, yes, you are eating way, way too little. The bare minimum for women is 1200 and men is 1500 or 1800 depending on your source). Googling protein shakes, they seem to range between 120 and 160 calories per serve (and I'm pretty sure the 120 one I found was before you add milk- which starts at 35 cal per 100ml). Oats are 178 calories per 50g (which is what I use to make porridge, so you probably add less), fruit it depends (the apple I just ate was 138g and 69 calories), applesauce similarly (google tells me about 100 calories a cup). And then looking to dinner, chicken breast contains 260 calories per 100g (which most people would consider a small serve), and obviously anything with it (vegetables, sauce, rice/ pasta/ other starch) has calories as well, including the way in which it's cooked (unless you steam or boil everything, which would be pretty disgusting).
You need to get a handle on how many calories you're eating, and how they relate to you (use this website: which will tell you your calorie allowance to maintain your weight, according to your stats and activity level). I'd suggest you also need a more balanced diet, if not for the sake of weight loss, simply for the sake of your health. I very much doubt protein shakes are meant to be meal substitutes, and if they are, certainly not for 2/3 of all your meals.