My house has become completely INFESTED with fleas, what can we do to get rid of them once and for all?

To get rid of the fleas, you need to enlist the cooperation of your neighbors. If they have dogs bringing fleas into the building, there's no way you can rid of them in your unit. I'd call a professional pest control company and have them treat both units. Then ask your neighbors to have their dogs dipped or treated for fleas. This should solve your problem. Treating just your unit would be like treating half a bed for bed bugs, it just won't solve the problem.