I don't know how bad your dizziness and balance problems are. You should get physical therapy to help it. The sooner the better, since the most progress is achieved in the first 6 months, but small improvement can occur years later. Everyone is different. My stroke was 4.5 years ago, and I have never regained my handwriting ability. I still have difficulty with balance and walking, and that was after months and months of physical therapy during the first 6 months and then again a year later. But I am far far better than I was originally because of the physical therapy. So don't assume that you will go back to normal without any help. Maybe or maybe not.
I am 48 and suffered 2 strokes in dec 2010. I have had the dizziness and balance problems like you are experiencing and found that over time they decrease gradually. Have you mentioned this to your GP. I would be interested in their reply.