As far as Elinor knows, she is the only woman in Edward's heart - although she is not absolutely convinced that he loves her. She therefore assumes that the hair must be hers, and takes it as proof of his love.

As for the issue of this being out of character, well, surely even the most sensible woman is allowed a moment of vanity, especially if she sees the man she loves wearing a ring that appears to contain a lock of her own hair? This also explains why she doesn't make a fuss about it - she is flattered that Edward would go to what would have had to be pretty extreme lengths to procure the hair, if it had really been hers.