A viral throat infection is going to make it difficult to tell what's what until you have got over it. it could, of itself, be causing the sickness and dizziness and it could also be affecting blood sugars, which just might make you feel a bit odd.
You say that your diabetic nurse said to "eat healthy". I wonder if she gave any more details or how you interpreted this vague remark. Much of the advice handed out by the NHS is of little help to diabetics and will do next to nothing to bring down blood sugars to a normal level, so you need to be looking round this site (I would advise the Low Carb Forum) and try the site, dietdoctor.com. Also, your DO need to test, for a while anyway. How on earth are you going to understand this disease and the effect of different foods if you don't?
My initial advice is to cut out all sugary things and try and get over your throat infection, then get yourself a glucose meter, start testing and moving towards a low (or lower) carb diet.
good luck
Sally