Is it normal to start a healthy diet and be so ill?

It's normal and I can explain what's happening with you. When you are used to eating certain foods and then make an immediate change to a different selection of other foods, your body natural responds like the way you described. Your body hasn't been given time to adjust to the change and this is how your body reacts to it.

I can relate to you because I'm on my own regimen too. My regimen consists of an 1,800 calorie diet of 3 small meals with 2 small snacks in-between (Totaling 5 times a day I eat) and 30 minutes of walking everyday.

Like many people, I found it hard to tolerate a diet because the food doesn't taste as good but that doesn't mean you can't find good alternatives. I have things to eat like Veggie Patties, Chocolate Brownies with Fiber, Fudge Bars with Fiber, Whole Wheat Cheese Chips, 100 Calorie Snackpacks, Lean Cuisines, Healthy Choice Meals and etc.

Exercise doesn't have to be a tiresome chore either. I like easy exercise and walking is as easy as it gets. Walking is the least fat-burning exercise (Which is why it's best to do it everyday for at least 30 minutes) but it offers as much health benefits as running. Walking reduces your risk for Alzheimers, Dementia, Heart Disease, Stroke, lowers Cholesterol, lowers Blood Pressure, strengthens bones, reduces stress, reduces anxiety, reduces depression and has many other health benefits.

Here are some tips to help you drop the weight -

1) Drink Green Tea. Green Tea has many Antioxidants and has been shown to raise Metabolism by as much as 4%. A Study was conducted with 2 groups of men both of which had the same diet with the exception of one group that drank Green Tea daily. After one month of study Scientists found that the group that drank Green Tea lost an average of 5.2 pounds while the other group that didn't drink Green Tea lost an average of only 2.6 pounds.
2) Avoid convenient transportation. Instead of driving to the Supermarket, walk there. Instead of taking an elevator, take the stairs. Taking longer trips to get to places will help to burn extra calories.
3) Get plenty of sleep. A person who sleeps 8 hours will burn an average of 500 calories. The less sleep you get, the less calories you'll burn.
4) Remember that you want to lose weight in fat. Dropping some pounds doesn't nescessary mean that your plan is working because the weight can be weight in Muscle Tissue, Water, Fat or Excrement. Make sure you're losing weight in fat (buying a Body Fat Measurement Device would help).

Before I started my regimen I weighed 200 pounds and now I'm down to about 183. My goal weight is 165 pounds and I'll be able to reach this goal by the end of the first week of May, 2012. What you're doing takes a lot of patience and I know firsthand that it is not easy to be patient with losing weight. Just keep it up and soon enough you'll achieve the weight/image you desire.

Goodluck and feel free to respond to my comment if you have further questions and/or want more advice.