I didn't have it that bad but I sometimes I'd sort of reel or stagger, and then steady myself. I never had to grab onto things. I never actually fell or came close to falling. But I thought it was odd that I felt dizzy. It was something new to me. I read it could be part of PAWS (post acute withdrawal syndrome) so I never worried about it. And now it's gone.
Yours sounds kinda severe though... not sure what that's about, but stay in touch with your doctor! Just to be safe.