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If he potentially ingested it 2 days ago, the odds are good that he will continue to do find, but to be safe, I would at least have him examined and have an abdominal xray performed. You may not see the stick on a radiograph, especially if the chewed it at all, but if there is any obstruction or blockage due to it, that may show signs. The biggest concern if he swallowed it whole is an obstruction or a perforation, but he is not showing any signs of either from what you describe. If he has not passed stool since then, an xray could insure that he was not getting constipated as well.
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