According to movie canon, he did not look this way onlyuntil after he came back with quirrelQuirrel. In the last movie, you are shown voldemortVoldemort killing Lily. He looks the same then, as well.
Also: with the snake, she was a horcruxHorcrux, one of the orginalsoriginals, which were likely created whilst tomTom was still young, as evidenceevidenced by the scene in the half blood princeThe Half-Blood Prince. So, it is quite possible that naginiNagini has nothing to do with it.