Is it embarrassing to date a tall girl?

Yes, it could be embarrassing to others if a short guy (<6′0″) is dating a tall girl (>5′8″), but only if you were to care what others think of you. If you do not care of others opinions of a small man dating a larger woman, then it should not be embarrassing to the parties involved.

At what age do girls stop growing in height?

Once girls start to menstruate, they usually grow about 1 or 2 more inches, reaching their final adult height by about age 14 or 15 years (younger or older depending on when puberty began).