You are a brave man. Although at a time like this you don't feel that you are brave. The reason I'm saying that you are brave is because you went through with what happened, survived the worst and still want to go back petting your dog. And other dogs maybe? ;) This requires a lot of bravery and courage.
With this bravery and courage that you are showing, it will be easier for you to get through your phobia. I have mentioned easier, but its not a here today, gone tomorrow thing.
Are your hands already healed? Or are your hands still at the state shown on the photo?
If your hands are still at the state shown on the photo, then you may want to sit up high and use your legs to play with your dog. If you find this method too degrading to your dog, then you can wait till your hands are healed.
If your hands are healed, you can sit slightly higher where your Jack Russell can't reach your face. Your phobia is with dogs going near your face and them having sudden movement I assume. So sitting where he can't reach you will assist you on this. Start petting him face-to-face. You know he won't bite your hands and that is a fact. Play a tug and pull game with your dog. You can start with some tug and pull toy that is long. And over time, shorten your distance between your tug and pull game with your dog. What you need to achieve here is to deliberately put your hands into his mouth and play tug and pull with him with YOUR BEAR HANDS. This is not going to be easy, as the fear will be there. But you can overcome your fear for the love of your dog.
The time to shorten the toy will depend on your comfort level.
The next fear you need to overcome is the fear that your dog will suddenly jump at you. For this, you can hug him and try to pull your face nearer to him. With you hugging him, he can't jump at you suddenly. You choose when to put your face near him. When you can look him in the eye and stick your face to his face, you are ready for the next step.
Play fetch with him for this step. If you are brave enough, you can skip the previous step and come to this step straight. Since you are playing fetch with him, you know where he will run to, you can squat down and deliberately hug him face on. Since he is running towards you, you will feel the feeling of dog suddenly coming to your face, but with your readiness. A few more times of this, you will find that you no longer fear him.