Sorry to hear about your problem.
Riding and staying on is definately do-able. I had a left sided hemiplegia at birth, so have always had a weak left side, but it hasn't stopped me from riding, indeed riding has helped with strength and coordination.
Also last spring I had a stupid fall and managed to tear my rotator cuff, I was back on board 6 weeks later but did feel vulnerable as it was still weak and painful. I still went to the breed show and did dressage, show jumping and working equitation, so don't dispair!
Horses are amazing and will easily adapt to being ridden one handed - (think of the Spanish Riding School, the cavalry and cowboys) or with one leg (e.g. sidesaddle) if needed.
The thing that really improved my riding overall was having a series of lunge lessons to develop a really secure, balanced and effective seat and if you can find a decent instructor I would really recommend this. I've also found using a gym ball in the house very good for improving seat and balance. And keeping up doing the strengthening and stretching exercises - which I'm less good at! A good sports physio will also help.
I don't know what your horse is like, but it's much easier to ride if they will go forward from a soft aid, or even a voice aid and then maintain pace by themselves, so its worth working on this for the longer term.
In practical terms before getting on again get yourself a big secure mounting block and teach your horse to stand still by it, if horse is fizzy lunge him first and maybe get a foot soldier to walk with you the first few times, or get someone to lunge you on him. A grab strap actross the d-rings or a hunting breastplate to hold are also good precautions.
Good luck with it and feel free to shout if you have any questons