You should be alarmed if you have nausea and vomiting. Diabetics sometimes suffer from nausea or vomiting. You may also have nausea and vomiting if you have ketoacidosis. Hence it is imperative that you monitor your blood glucose and ketone levels. Do go for medical help is discomfort persists.
Some other symptoms could be loosing weight or running a temperature. You must visit your doctor under these circumstances and take a record of your fever and blood sugar and ketone level test results. Some other symptom could be loss of appetite. If you do not take in enough calories, your blood sugar levels can come down causing dizziness. You must take the necessary steps to bring the blood sugar levels up.
Something alarming is when you notice high blood sugar levels that don't decrease with take extra insulin. Please consult your doctor immediately.