Allergies don't make you dizzy, it's the inner ear infection. That can be brutal.
I came down with vertigo (incapacitating dizziness), last May (the night the C's lost the lotto), and couldn't walk for 2 days and then could not have been able to play basketball for perhaps 6 weeks. It was crazy. Not sure exactly what Wallace has, but if it's anything serious - he won't be playing (or playing effectively) anytime soon.