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

Possibly Bursitis: It's possible you have developed a greater trochanteric bursitis. If it persists definitely see your PCP or orthopeadist.

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.