The axis has shifted (if that's the correct term), but not by 2.5 degrees, not by far. It was a very minute shift, more like 2.5 inches. And an axis shift doesn't make us drift into outer or inner space at all, you can perfectly stay on course around the sun with a 90 degree axis shift as well.
If the climate had changed because of such an axis shift, it would happen everywhere, not just in Canada and the US. But I can assure you that there's nothing extraordinary happening in Europe for the moment, and I haven't heard reports about it from elsewhere either.
Plus, as had been said, a 2.5 degree shift would be visible to every amateur astronomer, and they wouldn't all keep quiet about it.

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