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In brief: Sciatic pain. Yes. Ice is an excellent anti-inflammatory option. Try alternating moist heat to relax muscles and ice to reduce swelling. Physical therapy and stretching exercises are important additions to reduce the pain and prevent recurrence of the pain.
1 Physical therapy is often prescribed for sciatica.  Someone may receive special instructions from a doctor on dealing with back pain. Some will recommend using heat, others cold. One may also get information with pictures of back exercises and stretches one is expected to start when the pain improves.