I was also in Physiotherapy this year and I bought a stability ball to use at home. Its a large air filled ball that you can use to work your core muscles.
A simple balance exercise is to sit on the ball with your back straight and lift one foot off the floor and hold for 30 seconds. When you've mastered that, try doing it with your eyes closed.
Doing exercises that build your core muscles will improve your overall balance.
This polly esther isn't synthetic - she's au naturel!