Wow, I could have written much of your post myself! I had a spinal cord injury in 1995 and never did regain feeling in my legs or bum. And I have balance issues, too.
I have discovered that just about every activity is possible for me, but I do need to figure out how to accommodate my body. My GSD is close to 8 years old now. But he drove me crazy when he was younger. He was like the Ever Ready Bunny, he just kept going and going.
I played a lot of fetch with him. Indoors I would bury his ball in a pile of cardboard boxes and have him find it. I tried to think of things to do with him that exercised his mind as well as his body. I worked really hard on his obedience, so regardless of how excited or antsy he was, his response was rock solid. Walking him became so much easier for me.
I found some old agility equipment and used that in the back yard. I found a place to take him off leash where there weren't other dogs, so he could zoom around me while I ambled along at a much slower pace. So what if I drove there instead of walking. The point was to get him there, where he could run and I could walk. I use a cane when the footing isn't smooth (and sometimes when it is smooth, too!) and Tanner has gotten really good about not bumping into me hard. Thankfully he was never a jumper.
Keep trying different things! You'll eventually find some activities that work for both of you. It can be done. Just keep yourself safe first and foremost. The rest will follow if you keep working on it.