I've never had a problem with that since I always use my forearms to break the landing when falling forward.?
This, wouldn't really recommend it. It's better than sticking the hands straight out but you can still fuck up your arms. In comparison to your body mass, limbs are a weak point.
In the situation you described it's hard to fall the "ideal" way because you are out of balance and just holding on for dear life. The way you fell it sounds like you impacted the ground directly on the corner of your shoulder which can potentially snap a collarbone.
Best way to fall IMO is to let your body (not limbs) take the hit. Be a plank. Keep yourself tucked when you impact, but also have your muscles be somewhat loose. Don't tense up on impact, it just increases damage to the impact zone. The idea is to sort of be like a ragdoll, and "flop" as much as possible when you land.
The science behind this is that if an object can keep moving after impact it spreads the stress out over a longer period of time, resulting in less damage. As I said before though you cannot control all falls and some do just end in the dead-stop-slam which will do the most damage.
And just as a note, the most often time people get injured is when they bail last second out of something. If you commit and crash, you will at least be somewhat in control and be able to avoid the "oh shit flail". <--- that thing is awful since you can't really influence or dictate how you land once you are trapped in it.