Dizziness is more closely associated with shock rather than stress. When you feel overwhelmed you also start to feel emotionally and physically out of place, and that's when dizziness sets in.
At some point stress may be so overwhelming for either the mind or the body that a small shock sets in and causes dizziness. This doesn't have to be a big thing. For example, you have a deadline you have to keep and work like crazy. As the deadline creeps closer, you realize that you might not make it in time, and this thought makes you a bit dizzy.
Prolonged stress makes you focus on a small part of your life and mostly ignore everything else. When the 'everything else' catches up, it is often quite overwhelming and causes even more stress - and so on in a downward spiral.
The short term cure for stress related dizziness is to sit down for a moment to relax and gather your thoughts, and go for a short walk later in the open and take deep breaths. As long as the stressful situation persist, so does the possibility of dizziness at any time.