The most important issues on this diet with dizziness are...
Getting all your water?
Getting all your salt?
Low blood pressure can result in dizziness, and salt and water are major components.
Also, are you taking your potassium pills? Your electrolytes need to be balanced with the salt and water. Low electrolytes often make me a little lightheaded.
If all these are good, then you may want to see a doc and have your blood sugar checked. There is a possibility you're not getting enough calories. But don't make that decision until it's been checked by a professional.