Definitely go and see a physio and try out different types of sticks and handles. My OH has MS, he has foot drop and struggles with balance - he can topple over standing still. He used a walking stick with a slim handle for years.
Due to recent surgery he has tried a stick with a Fischer handle; the difference is remarkable, he is much more stable and walks more 'up right'
Bear in mind the ferrules (the bits on the bottom). Some are better for uneven ground, some better for concrete, smooth floors etc. We are struggling to find ferrules that fit sticks with Fischer grips for uneven ground, necessary for us as we live in the countryside.
In the meantime, i hope they get to the bottom of your other health issues as they may sort out your balance. Please do not give up x