Attitude matters. When taking pain medications (and my daughter has taken innumerable pain meds with doctors' supervision), it's important to watch your attitude and your words.
By that I mean, education and moderation are important. You don't just casually tell your daughter to take a pill. You don't leave the pill bottle lying around. Since she's 10 and not 4, you take the time to tell her that pain medications can be helpful but it's extremely important to follow the doctor's orders, and follow any of the cautions on the bottle (pharmacists often add stickers to the bottle that say things like "don't drive while taking this medication" or "take this medication with food [or plenty of water"). Help her carefully look at the bottle of pills and the pharmacist's leaflet that came with it.
Help your daughter evaluate her pain level (use that smiley face/frowny face/angry exploding face chart), and help her keep track of the time she took a pain pill. Note it on a white board or in a notebook or something. That way she'll say "oh I just took one 3 hours ago and it says one every 6 hours", or "hey yesterday I needed 3 pills but today I only needed 2. That's improvement".
And teach her how important it is to keep her pain pills in a very safe place, and never to share them (even with a family member). Don't just tell her that the pills will make everything better, but that they are a tool in the whole toolbox of recuperation (which includes rest, following all the doctor's orders concerning how to sit and how to move in order to lessen the pain and not aggravate the injury, and anything else the doctor instructed. Read through the papers you probably got at the emergency room or at the doctor's office (they often give you a pre-printed page called "so you have a bone fracture" or "now that you've been diagnosed with a concussion" or "what is strep throat?", etc).
She probably won't be on pain meds for a long time. But pain is extremely physically fatiguing (my daughter went to a pain management clinic for a long time and we learned about the side effects of pain), and it can be depressing, and if it's not managed well it can interfere with recovery.
If your attitude is that the pain meds are one tool in the toolbox, or one arrow in the quiver, and if you speak honestly with your daughter about medication safety and proper respect for powerful medications, she'll develop a healthy attitude towards them and not think of them as the answers to everything (like some kids grow to think that any meds will help them stay more alert even if the meds are for their diabetic grandmother or their sibling's chronic illness).