When dieting, you run the risk of getting low blood sugar and low iron (especially given your age and that you are female).
I would suggest you either borrow a glucose monitor or go to the doctor to have your blood sugar taken (especially when you start feeling the tingling, weakness and like you are going to pass out). To prevent it from happening, you should eat something high in protein such as cheese and crackers. Avoid carbohydrates as your first meal of the day as this will cause a spike that will cause you to drop later on. I am not sure what meal plan you are on for your diet, but I would juggle things around to keep an even protein level throughout the day and most of your protein early in the day.
Anemia can also make you weak and shaky. Often people on diets tend to not get enough iron rich foods. You will likely need to have a doctor check this as well but a home test you can do is to look in the mirror at the outsides of your ears. Are they pale? Pale ears indicate the likelihood of anemia.
Drastic reduction of certain foods in dieting can wreak havoc with our bodies but I do want to congratulate you on your substantial weight loss. You just may need to supplement or switch things around a bit.
Take care and let us know how it goes!