Sprains and fractures share many symptoms, including pain, swelling, and bruising, so it is genuinely difficult to distinguish them at home. Features that raise concern for a broken bone include obvious deformity or a limb that looks out of shape, inability to move or bear weight on the part, pain that is sharply localised over a bone (rather than over soft tissue), a grinding or cracking sensation at the time of injury, and numbness or coldness beyond the injury.
Because an untreated fracture can heal poorly, the safest approach when these features are present is to have it assessed and X-rayed. In the meantime, keep the limb still, avoid putting weight on it, and apply a cold pack wrapped in cloth.
Seek emergency care immediately if the bone is visibly broken through the skin, the limb is cold, blue, or numb, there is heavy bleeding, or the injury followed major trauma. For less severe injuries that do not improve within a few days, see a doctor, as some fractures are subtle and only show on imaging.