Dizziness/vertigo is a common problem with people who spend long hours sitting in s specific posture , specially people who work long hours on computer and internet.
This feeling is associated with posture change, and with the movement of neck in specific directions. Some times gets confused with low blood pressure or hypoglycemia (low sugar level of the blood) but it is not specifically the case.
I have experienced personally among some programmers and webdevelopers, who spend hours working on their bed/ couch for many hours in a go, with a very much improper posture of their neck , which keeps on bending forward, and also the shoulders muscles remain tensed because of typing.
The issue can even lead to the damage to the vertebra of the neck and thus causing long term damage to the neck and spinal cord.
The solution is probably simple. That is, keep a proper posture while working on computers or what ever type of work you do.
The neck should not be bent very much for long and also the shoulders should be kept at ease.
Take frequent breaks during work, to release tension from your muscles of neck, shoulders, arms and eyes.
Exercise daily, normal jogging and pushups might work. Swimming is the best in this case, if you make a habit of regular swimming, you will not encounter this issue probably. However there are several specific exercises for neck muscles too to relieve the problem.
Massaging the neck muscles gently and smoothly also relieves the problem and may help in stabilizing the persons dizziness and vertigo issue.
You should consult your physiotherapist for details on what should be done specifically in your case.