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On rest and recovery days it is important to avoid doing the worst thing you can do for your body... nothing. Examples of rest and recovery activities are walking, static stretch exercises (after a warm up and loosening up period), dynamic stretching, swimming, water running, and riding a bike.
If you are unable -- or unwilling -- to take the day off, you should exercise at a relaxed pace in another sport that stresses muscles other than the ones that feel sore. Aspirin will reduce the swelling of damaged muscles but it won't increase the rate at which the tissue heals.