You’re just lucky it was a cheap Yoyojam… If it was a full sized metal you’d have lost your head.
I found adjusting my breakaway technique helps a lot. Rather than throwing the yoyo out and to my right, I throw it down towards my left foot. It’s more of a dramatic horizontal motion than a sweeping loop, so if the yoyo does snag, the amount of forward momentum takes some of the power out of the swing so it doesn’t really make it far enough to hit my face. I’m not particularly advocating this technique, it’s just what works for me.
Also, lean back. If you throw a breakaway with your face in the flight path, you’re asking for trouble. Adjust your stance so that even if it does snag, you shouldn’t be in the way.
Busted knuckles are just a given really, not much you can do apart from use thinner string and watch your string wraps.
And finally, the #1 rule: Never put aside a knotted yoyo thinking you’ll unknot it later. You wont, and you will forget, and you will take a chunk out of your face.