Hi viceroy:
I wouldn't call it "normal" to have dizziness after diving, but it probably is common, particularly in new divers. I would say that the most common reason to have persistent dizziness after surfacing is probably inner ear barotrauma. If a diver has difficulty clearing their ears due to inexperience, inattention, or congestion, lack of clearing or forceful clearing can cause pressure injury to the delicate inner ear structures that control balance. The symptoms can start immediately after diving or be delayed. Auditory changes such as hearing loss, fullness in the ears (like you have water in your ears), ringing in the ears, etc. are often present too, but don't have to be. Inner ear barotrauma can be avoided by clearing ears and sinuses gently, early, and often, and avoiding diving with congestion. New divers frequently have problems with clearing.
Another cause for dizziness after diving is alternobaric vertigo. When one ear clears better than the other, there can be a difference in the pressure between the two ears- most often on ascent. Symptoms usually occur during the ascent or within 2 minutes of ascending, and usually only last 10 minutes or less. There may be "squeaking" or "crackling" noises in the affected ear as the pressure equalizes. Avoidance of alternobaric vertigo is the same as with inner ear barotrauma.
Decompression sickness with either DCS of the balance mechanism of the ear or of the part of the brain controlling balance can cause dizziness after diving. It can occur many hours after ascent but usually sooner, persists for more than a few minutes, and can be associated with other signs or symptoms of DCS.
Cerebral arterial gas embolism can cause dizziness after surfacing. Symptoms usually begin very soon after ascent, persist for more than a few minutes, and are commonly associated with other signs and symptoms of a decompression injury. Avoidance of CAGE involves preventing air trapping on ascent such as from breath holding.
HTH,
Bill