@moredoll did you actually read your own fucking link? It says to call an ambulance if you suspect the child has broken their neck or spine!! Not an arm.
Or call an ambulance if child in utterly severe pain which I don't think the OPs child was.
Yes, I read my own fucking link. What a pity you didn't.
Also a shame you forgot the good manners your parents struggled so hard to instil in you.
For the removal of doubt here is the link from the NHS website giving advice on broken bones in children.in full;
Broken bones in children
If you think your child's neck or spine may be injured, call an ambulance. Don't move them. Unnecessary movement could cause paralysis.
A bone in your child's leg or arm may be broken if they have pain and swelling, and the limb seems to be lying at a strange angle.
If you can't easily move your child without causing pain, call an ambulance.
If you have to move your child, be very gentle. Put 1 hand above the injury and the other below it to steady and support it (use blankets or clothing if necessary). Comfort your child and take them to hospital.
If you think your child is in pain, give them painkillers, even if you're going to A&E. Follow the dosage instructions on the label
The ambulance operator will question you so if your child has a pain free break (unlikely) they might possibly advise you to bring the child in if you can if they are busy. Maybe.
The role of a trained first aider is to assess whether or not medical advice/treatment should be obtained.
I cannot stand people who think children should suffer unnecessarily. Don't understand them and don't want to.