I noticed your questions were closed-ended questions: questions that require a yes/no response. These are less effective at showing empathy and warmth.
You're most likely not really interested if their arm is still hurting. Only a doctor would be concerned with that. By asking, you are expressing concern for them. They can give you details after that if they want. I think the key is to simply ask something like "How are you doing?" or "How are you feeling?" and leave it open ended.
Let's say my friend Joe broke his arm on Monday and on Tuesday Sally leaves me a message to let me know. I call Joe Tuesday. First Call Dialog:
Me: "Hi Joe it's CoolHandLouis."
Joe: "Hi man."
Me: "Sally told me you broke your arm. Dang (ouch, wow, sorry, oh no, your-choice-of-quick-empathetic-comment). You ok?"
<--- OR --->
Me: "Sally told me you broke your arm. I'm really sorry to hear that. How are you doing?" (This is more formal.)
Joe: "Yeah it was stupid I caught the curb and fell over the front of my bike and hit a fire hydrant."
Me: "Oh man. I hate it when that happens..."
Joe: "Heh... yeah it sucks."
Me: "How's your bike?"
Joe: "It's alright, just scratched up a bit."
Me: "Hey next time break your bike and scratch your arm, ok?"
Me: "You know, those fire hydrants... they'll win every time."
Joe: "Yeah that's for sure."
Me: "Let me know if you need any help with anything. I mean, I'm not going to be scratching anything for you..." (Joke is very informal. Only with someone I know well and have joked with before.)
Joe: "Ha! No I'm good."
Me: "Seriously, if you need anything, give me a call."
Joe: "Ok but I'm good. Thanks."
Three days go by and I call him back. Second Call Dialog:
Me: "Hey Joe."
Me: "How are you doing?"
Me: "I just wanted to call and find out how you're doing." (NOTE: This is more formal but sincere, and good for just about anything wrong.)
Joe: "Oh I'm doing alright. Just watching a lot of TV."
Me: "How's your arm?"
Joe: "It's feeling better, thanks."