Could you explain the form of dizziness/vertigo you suffer from? Is it rotational vertigo (spinning), and does it involve vomiting? Or is it loss of balance and non-rotational perception of movement?
I think the question you are asking is one of those 'how long is a piece of string' questions. A lot depends on the nature of the infection you have been suffering from. But it is perfectly normal for residual dizziness/loss of balance to last even up to several months after the worst of the vertigo has subsided. That's not to say that it will be several months in your case. Everyone's scenario is different.
I trust you will have already seen ent specialists and probably have a good idea about the nature of your infections. If so then all you can do is to be patient, and know that it will pass in it's own time. There is little you can do to speed up the process other than to follow the usual inner ear dizzy advice, such as avoiding caffeine and sticking to a low-sodium diet.