The significance of "y"
Looking them up in the Oxford Dictionary of English Language, your comes from Old English ēower, related to the genitive of “gē.” It states that it's of Germanic origin and is related to German euer.
While our comes from ūre, which is also of Germanic origin but is related to English us and German unser.
This should be proof enough that the two are not related and the similarity is some sort of coincidence.