Congratulations on your active lifestyle! Unfortunately, running can be associated with multiple pain syndromes, including pain in the hip. Most of these syndromes are overuse injuries that can be remedied by stepping down the level of your training, doing some physical therapy, cross training in lower impact disciplines, and making sure you wear good athletic shoes (for example if you are an over pronator, this is something that can be fixed with the right pair of shoes).
Pain that radiates down the side of the hip and thigh towards the knee is most likely to be iliotibial band syndrome, one of the most common pain syndromes in runners. It is usually from iliotibial band tightness, which can be helped with stretching exercises, or by weakness of the hip abductors (move the hip out from the body), which can be helped with strengthening exercises.
Pain that is primarily in the back and buttock region of the hip is more likely to be piriformis syndrome, resulting from tightness and too much internal rotation of the hip. Treatment takes longer, and generally involves deep massage, rest, and exercises to try to strengthen the external rotators.
Talk to your trainer and your primary care doctor
if you have more questions.