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I think that you are doing the right thing by placing ice packs. However I would strongly recommend that you should go to the A & E to have you examined to make sure everything is fine and to make sure there is no internal injury in the head.
If you fell unconscious or had bleeding from the ear or clear fluid coming out from the nose then again that is a clear indication to go to the emergency as it indicates a fracture in the skull.
Meanwhile I would also recommend that you should take over the counter anti inflammatory medications like ibuprofen 400 mg three times daily which will help with the pain and swelling.
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