I haven't had any dizziness, but my balance was apparently a bit off (not a lot) following my injury. According to my osteopath, my balance now seems OK (keep in mind that I'm now into my 14th month of recovery).

I was much more sensitive to all kinds of things earlier in my recovery. It is only more recently that I have become more comfortable with massage therapy and various other activities. My feeling (not based on any hard research, just my own experience) is that it's better to hold off on most activities until you can appropriately tolerate them. Pushing generally made me feel worse, although some gentle pushing through (i.e., incrementally) may be appropriate in the later stages of recovery.

Fwiw, another massage therapist / osteopath I know said that she recommends holding off on treatment until symptoms have largely resolved.