On the age of the Jew's harp and blues harp (harmonica), the Lark in the Morning catalog has a few things to say. Here are some quotes:
"The sheng, also called the Chinese mouth organ, is one of the oldest Chinese instruments. It has a history of thousands of years and its manufacture and use was reported in ancient Chinese history. The sheng is the instrument that inspired the invention of the concertina, accordion and harmonica, and uses the same technology of metal reeds that vibrate as air passes through them. It has a wonderful sound, and can play melody and chordal accompaniment all at once."
"Kaen; Thai Mouthorgan - The Kaen is the oldest form of the freereed family, the great great grandaddy of the harmonica and accordion. This type of instrument goes back to at least 1100BC (the harmonica and accordion only go back to the 1830s). Made of bamboo with a brass reed in each tube."
They also list two or three types of bamboo jaw harps (as they call them) from Asia, without giving much history (also a few modern models). However, the Jew's Harp Guild website has a brief history including archaeological finds of the instrument dating back to AD 900 Japanese iron models.
So in one form or another both instruments are pretty ancient. The Jew's Harp in it's modern form outdates the modern harmonica by a wide margin. As for the origin of the term "blues harp", I don't know specifics but I do know that Hohner sells one of their standard 10-hole models under that as the trade name (another being the Marine Band).