Do I need to differentiate between the left or right arm if it doesn't matter if it is their left or right arm? Example: If I am prone on the ground and I use both hands to lift myself up and one of my arms gets pulled away or slips, should I worry about saying it was my left or right arm? "Then my arm was pulled out from under me!" "Then my left arm was pulled out from under me!" I think this could be applied to any object or body part. Like Someone poking another person's eye. "Then he poked me in my eye!" "Then he poked me in my right eye!" Is the more specific example necessary when the exact detail is unimportant (or at least appears to be)?
Here's an actual line from my story. "He tried to push himself up but his left arm was yanked away. " I'd prefer to do something more ambiguous like: "He tried to push himself up but his one of his arms was yanked away. " I like this one because the reader gets to use whatever arm they want. Left or right handed people favor their own hand when asked to pick one. If I was reading about a left handed sword fighter, seeing left hand this left arm that would seem odd to me (I think).
I don't think you'd normally need to specify which arm is doing something. Not unless it actually matters. It's the sort of detail peoples' brains will instinctively fill in. "His arm was yanked away." Is fine. I don't think the "one of" is needed either. It's clear you're talking about one arm already.
What @plothog said. I wouldn't specify unless it's relevant. At least I wouldn't think the character's one-armed, unless you've mentioned it before.
If it's important, you could mention later the person having trouble with a task because they are right handed and hurt that hand. Otherwise, I think it sounds more natural to just not mention it. On the other hand, if this was POV character observing another character hurt his/her arm, you might mention if it was the left or right. Some people notice small details of other people.
