Right side Hip pain after running I went hiking and the next day pain started right side hip?

Varies. There are a number of possibilities, one of the more common is a tendonitis of the tendons outside the hip. This condition has a number of names including TFL syndrome. Treatment involves stretching, warmup, ice down. There are other potential causes as well, so don't hesitate to be seen.
Possibly Bursitis. It's possible you have developed a greater trochanteric bursitis. If it persists definitely see your PCP or orthopeadist.