First of all you need to gain a class 1 medical and tell them about your hands. If you successful then you will know you are fit to fly, if not then you can make a decision to stop the professional flying route.
During your training there will be times when you will question yourself and perhaps fail, this is the same for all of us. Having a "can do" attitude is needed and you can get help with this from professionals, but you must have the seed of this first to see it through.
Multi tasking is perhaps the big issue but training will help you learn how to do this when flying, the issue might be when you come to instrument flying as the mental demands are very high indeed. Nevertheless training and more training will overcome this unless you not capable of taking this on and have reached your limit.
My best advice is to have a pre assessment done, which are done for military aircrew as part of the selection process better to check this out first. In fact consider the military route first and get the government to pay for the training, this is not for everyone but is perhaps the best economic path in today’s hard times. Good luck
