Nope. Charles is the only Prince of Wales as of now. Once he becomes King (ugh), he should bestow the title on William, as he is next in line for the throne. Charles was created Prince of Wales in 1958, although his investiture did not take place until his mother crowned him in 1969. In 1970, he took his seat in the House of Lords.
The official website for the UK Royal Family says, "Prince Harry's official title is His Royal Highness Prince Henry of Wales."