I'm allergic to those things to. Most table sugar comes in the form of beet sugar (not sugar cane, as is commonly assumed), so there is a chance you have a sensitivity to the beet family. This is not an unusual food allergy. Beet family includes beet sugar, beets, spinach and chard.
A lot of processed foods have high fructose corn syrup, which is definitively shown to harden arteries even in small amounts, and corn is also a common sensitivity to those with food issues.
The question is, can you have other kinds of natural sugar like fructose (from fruit) and glucose (from honey). There is no such thing as a glucose allergy, as far as I know. Glucose is the most easily absorbed food, period. It requires no digestion or breakdown, however it quickly spikes internal glucose levels. Nevertheless, you can probably eat fruit and processed foods containing fructose unless your doctor says otherwise. There are more than two dozen forms of sugar (http://www.sugar.org/sugar-basics/the-other-26-sweeteners.html) and I find that I have trouble with just about all of them.
As for proteins, good news, high protein foods have little or no sugars so that's pretty safe -- unless of course sugar is mixed in (bacon, cheesecake).
You might consider a Paleo diet, which eliminates all grain, beans, dairy, and sweets, and is great for building muscle and losing fat. It is a diet that centres on dark green veggies and flesh. The book that seems to be all the rage is Paleo Solution by Robb Wolf. IMHO it is not well written and they guy is annoying, but it gave me the info I needed to get started.
A raw raw foods diet also eliminates the "bad" foods for you. But again, you would need to get educated to do it. (See Raw Power by Stephen Arlin)
Or just eat as you did and modify to replace dairy with eggs, beans, nuts, meat. Replace wheat with gluten-free breads. Only eat sweets that have safe sugars, or just give up on sweets. Lindt 85% dark chocolate is nearly sugar free and seems to satisfy my sweet urge.