@fify, @ddljohn-- Great tips!
I get headaches and dizziness during sinus infections. When it happens, first I make sure to drink more water. I always keep several bottles of vitamin water and electrolyte water in the fridge. Then I go outside in fresh air. Somehow oxygen helps dizziness and just makes me feel better. Smelling a lemon or an orange makes me feel better too.
If you are constantly dizzy though and these don't help, I suggest being checked out by a doctor. Dizziness can also be a sign of more serious neurological or metabolic conditions.
My aunt used be constantly dizzy and after having a blood test at the hospital, she found out she has hypoglycemia. It's when blood sugar is always lower than normal. The doctor said that if she hadn't been diagnosed and treated, things could have gotten a lot worse. Hypoglycemia can apparently even lead to a coma if it's untreated. Dizziness is definitely a sign that something is off.