This is a relatively common sensation that meditators in general experience. Nothing to be worried about. As far as the dizziness is concerned, different people react in different ways. Whatever dizziness you're experiencing is temporary and probably due to your relative unfamiliarity with this phenomenon. It should go away as you become more familiar with this.
You may want to read a previous post here
for more information. This type of question has been asked several times before.
All the best,
"The gift of truth exceeds all other gifts" — Dhammapada, v. 354 Craving XXIV