At 15 months an arm fracture is unusual if there has been no specific trauma (fall from bed / lounge etc) It is more likely to be a pulled elbow. It is usually caused by being picked up by the forearms rather than the upper arms or swinging them by the arms. Some kids are more prone to it than others.

Is there any swelling / bruising?? Feel up the length of the arm to see if there is a sore spot. See if you can move her non moving forearm by turning the palm from facing upwards to downwards (or vice versa). If any of them cause her pain you might be better just going to ED around 8am - particularly if your GP closes early on Saturday or doesn't do plasters. ED can xray, review, plaster (usually a half plaster) if needed and refer you to an orthopaedic specialist if needed. They can also put the elbow back if they think that is the problem. Good luck!!