During the acute phase of a soft tissue injury, when there is swelling and inflammation, cold packs/ice are actually recommended (along w/ elevation) to reduce the swelling.
Heat is more typically used in chronic injury or in acute muscle spasm.
Tiger balm will not do anything for dislocations or torn structures. Its active ingredients are the same as those in BenGay and all other "heat" causing ointments that work to distract you from pain by creating local sensory nerve irritation.
While cold is used to stop swelling in the short term
it is not good for joints and contributes to the buildup of fluids (water on the knee). To facilitate the healing process, restoring the integrity of the joint and flexibility, heat is required.
Tiger balm will do wonders by encouraging blood flow. Contrary to the statement that it will 'distract you from pain' (absurd), it will alleviate
pain without the use of invasive medications.
I know that there is a lot of swelling with that dislocation. As soon as you can be weaned off of the ice, my advice is intended to get you back in the dojo with good knees.
I've been through and seen it all from Aikido to football (soccer) injuries.