I am new here but I know exactly how you felt. I had almost the exact same thing happen to me this summer with my mule. Merle was acting up that morning when we were saddleing up for a trail ride ( been riding and camping for a week and it was the last day.) and he was just not acting right. Well about 4 miles into the ride out of the blue he threw a "mule fit" next thing ya know I was off center in the saddle trying to straighten up at a dead run down the trail passing 4 other horses. Needless to say I unfortunately, stayed in the saddle untill we passed everyone so that they all got great view of me bouncing along the trail. That was the first disaster, the second one of the day, happened 2 miles later in almost the same way. I was really lucky though... I only ended up with a few broken bones and some really wicked bruises.
Two days later is when I found Harley and switched from mules to horses. He is awesome and is "moody" every once in a while too but I wouldnt trade him for the world. Harley threw a fit once out on the trail and I stayed in the saddle that time thanks to the lessons I learned from Merle.
Everytime I think about it I can't help but remember what my cousin and best friend told me the next morning when I couldnt hardly move.
"There ain't a horse that can't be rode, and a rider that can't be throwed."
I am really glad that you werent hurt badly and had the courage to get right back on and ride again.