Your address was not kept up to date. The letter went to the wrong address - ah well.
See www.gov.uk/apply-national-insurance-number - google it yourself because you should never trust another persons link.
The page has all you need.
Have you been working for over a year? If so it'll be on your P60 form. Also, when did you turn 16? It can take several weeks I think. You don't need the card you just need the number so you can just ring them up go to