The high kick is thrown slightly different from a body kick. Near the point of contact the leg should change direction from upwards to downwards dropping the shin on the head or neck. Many trainers say not to throw head kicks in the early rounds, but instead to wait until the later rounds when your opponent's hands start to drop due to fatigue. However, while this is a great strategy, it is best to be reactive and throw one when the opportunity arises. You can also use faints to draw your opponent's hands away from their face, creating an opening.
It is not uncommon for people to struggle with high kicks especially if they have taken up Martial Arts later in life. If this is the case practise the kick slowly and build the height up gradually. A special video specifically for kicking flexibility will be available soon.