No there are no eggs in candy canes.
So if you're allergic to eggs then you can safely eat candy canes.
I've heard that years ago candy canes did contain eggs but now the candy canes made today do not contain any eggs.
I do know for sure that Spangler brand candy canes do not contain any eggs.
And most of the candy cane brands today do not contain any eggs either.
The candy canes also do not contain gluten, whey, soy or milk.
So if you allergic to those ingredients as well then the candy canes are okay to eat.