In Healthcare two common explanations would be used. Pain is a response almost always (unless by an outside force) towards a lack of oxygenated blood. The pressure that comes with the altitude could potentially cause some change in pressure of the blood, or a thrombosis (stationary clot) has gotten loose and has gotten stuck in the arteries of the arm which which is then called an embolism (traveling clot). The pain could potentially be the clot breaking off or the clot sticking.
However remember that scuba diving also occurred. In some circumstances a rapid pressure change can cause something called an air embolism ( clot caused by air). With nitrogen bubbles either causing a blockage or they are deposited in the tissues of the elbow which causes something called decompression syndrome or the "bends" (because it likes to happen at the joints.).
