Was AD started at Christ's birth?

No. The AD system was INVENTED in 525 by Dionysius Exiguus, though it wasn't much used before the 8th century. Nobody is quite sure what Dionysius based his calculations on, but he was trying to date the Christian Era from the Birth (or possibly the conception) of Christ. What is certain is that he got it wrong. Jesus was born at some date between 12 and 4 BC. Fopr more detail, see http://en.wikipedia.org/wiki/Anno_Domini.