If you currently have hip pain, High Intensity Interval Training should not be your priority. First, you want to ensure you are capable of high quality pain-free movement.

Once you have good pain-free movement and range of motion, you can start to expand on the speed and intensity with which you move.

Remember that going from 0 to 100 MPH is never a good idea. Progress should start from a walk, then jog, then run, then run fast (over weeks or months depending on your situation).

Always listen to your body. If you are getting pain / irritation then you might be going to fast too soon.

Think LONG term with your progress.

The specific style of HIIT that feels best for you will be highly individual, so you will simply need to experiment with what works for you.

You can do interval training using any modality:

-Running

-Hill Running

-Strength Circuits

-Swim

-Bike

-Calisthenics etc

Experiment with whatever variations give you a good workout but don't leave you crippled with soreness or with an inflamed and pissed off hip!

Whatever the version of HIIT you implement, you always maintain proper form. Bad form may be passably okay in the short term, but it is invariably bad in the long term.