I'm glad you had a safe adventure; others haven't. SAR members can probably relate having to rescue injured climbers (or dead climbers) who lost control while glissading. While on Inyo SAR I was involved in a body recovery in the same area you were glissading; climber loss of control and killed on impact with a rock.
I don't know your level of experience, but yes, your self-arrest technique could use some improvement...practice, practice, practice.
For the less-experienced who read this forum, here is an excellent video from the British Mountaineering Council:
https://www.youtube.com/watch?v=LM3xLshmNnkA few points they didn't dwell on:
1. Never attach the ice-axe to yourself with a sling. If you lose the axe while out of control, you can end up with a deadly instrument flying around you. This happened to me on the Palisade Glacier. I was fortunate to walk away uninjured.
2. Never, never do a standing glissade. This is nothing but a possible ticket to the E.R. It happens a lot - broken ankles and legs.
3. Get self-arrest instruction from a competent professional. Take a basic winter mountaineering course.
I realize that some in this forum will take exception to these recommendations, to which I say "too bad".