Sorry about your accident, I hope you are all right.
You should try to lean towards the turn to turn faster while counter-steering. (Counter-steering essentially makes the whole bike lean, so it helps if you yourself shift your weight a bit towards the turn, check MotoGP)
When riding a bicycle or a motorcycle, counter-steering is a method of initiating a turn by a small, momentary turn of the front wheel, usually via the handlebars, in the opposite (counter) direction. This moves the pivot point (the wheels' contact patches) out from under the center of mass to establish the lean angle for a turn. While necessary at all speeds, the need to counter-steer becomes more noticeable as speed increases.
Hence, to turn to the right, the rider first throws the bike off balance by momentarily pointing the front wheel slightly to the left. The center of mass of the bike plus rider will continue in a straight line, but the contact patches of the tires move to the left with respect to this straight line
As the desired angle is approached, the front wheel must then be steered into the turn to maintain that angle or the bike will continue to lean with gravity, increasing in rate, until the side contacts the ground. This process usually requires little physical effort, because the geometry of the steering system of most bikes is designed in such a way that the front wheel has a strong tendency to steer in the direction of a lean.
The actual torque the rider must apply to the handlebars in order to maintain a steady-state turn is a complex function of bike geometry, mass distribution, rider position, turn radius, and forward speed. At low speeds, the steering torque necessary from the rider is usually negative, that is opposite the direction of the turn, even when the steering angle is in the direction of the turn. At higher speeds, the direction of the necessary input torque often becomes positive, that is in the same direction as the turn.
Source: Wikipedia, Our Mighty Saviour
Maybe these two videos will help you understand counter-steering better. The first one explains the theory and the second one (fast forward to about 2:20 min) is just a demo.