How fast can I increase my level of fitness without getting injured?

Since you have a history of injuries you need to be careful. Do some cross training. You can bike and swim. A good exercise is to run in deep water so that you can not touch the bottom of the pool. Make sure you have good shoes that support and cushion you. You may need some insoles to help. Running and walking every other day should be okay, now you are going out every 3 days which is a long recovery period. Warm up and stretch before running and cool down and stretch after running. Often injuries are caused by tightness that occurs because we do not loosen up the muscles after they become shortened during exercise. Try some mage to help break up the muscle cells sticking together. When you get back into the gym start doing total body work and lots of abdominal and core muscle work. Some injuries are because of muscle imbalances.