Impact with a rock face while climbing can cause muscle injuries which result in internal bleeding. Such injuries are called contusions or muscle bruising.
The affected area of the body is often extremely painful and becomes hot and swollen. A useful aid here is a RICE bandage (R=rest, I=ice, C=compression, E=elevation). In other words, a cooling compression bandage.
You can cool the area by making a cold pack out of a disposable glove filled with soil containing plenty of moisture or water. With the glove on your hand, dig up a fistful of soil from the moist ground. Then turn the glove inside out over the soil and tie a knot in it.
The accident victim can place the improvised cold pack on the painful area without removing any clothing. The first responder can then tie the cool pack in place using an elastic bandage and firm pressure.
Compression helps to prevent further swelling of the injury. At the same time, cooling helps to reduce pain. You can now make a joint decision as to whether descending or rappelling is possible or an organized rescue is required. If you have to wait, ensure the accident victim is warm enough and well looked after.