First and foremost: I would strongly encourage you to visit a doctor before you decide to take on any sports (and after picking a certain Martial Art). They know what is best for you.
Which Martial Art to choose is a typical question but as much as all Martial Arts share a lot of common features, they vary from Art to Art, from style to style and even from within the style because the most important part of your Martial Arts training is your Master/Teacher combined with his techniques and exercises (reference).
You should know that we are all biased and unfortunately no one can try all Martial Arts.
However a good start might be to look around your area for the Martial Arts classes that it offers. Visit the class, talk to the Master/Teacher. I am sure they are more than happy to discuss their interpretation of the Martial Arts philosophy.
Personally I come from a Kung Fu background (both Northen Shaolin Chan, Jing Wu (Chin-Woo), Wu-Dang, Taiji, San Shao (San Da), and Krav Maga). Thus I am more biased towards those.
Because of your disadvantages I highly recommend to not engage in any grappling/throwing/lock-joints (such as Judo, BJJ, Aikido etc). These sports focus on throwing the opponent on the ground and you cannot afford that. Also they focus on the strengthening of joints, which in your case it might make it worse (again, I am no doctor).
What I suggest is to try "Internal Martial Arts". They focus on coordinating your body with your conscious and unconscious mind.
Taiji is a good example. You have plenty of exercises that improve your reflexes, but unlike external Martial Arts, here you learn by doing very slow movements, which deepen your understanding.
Please keep in mind that the goal of Martial Arts is not to kick ass, but to have a deeper sense of being and understanding your body.
Also in Wu-Dang styles (such as Taiji) you learn animal stances and forms (how cool is that? :D )