Hello from across the pond, I live in New Zealand.
I am sorry you are having these issues with your hip. The first thought that came to my mind was a dislocated hip or impinged nerves in your lower back. In either event, I feel a good chiropractor could be of some benefit, I know mine helps me when I have those issues.
If you have a misalignment or pinched nerve, you certainly can have the pains you are having, a few adjustments should have you feeling better in no time.
Hope you feel better soon. God bless you.
You must rule out an underlying condition called femoroacetabular impingement, or FAI, which could be
exasperated by overdoing it in yoga, possibly unknowingly grinding the hip bones with the potential of causing joint damage and later developing osteoarthritis.
So please look up FAI and see if this makes any sense.
You are very young, but when premature wear of joints due to the extreme range of motion (often combined with impingement) is taking place over time, it can bring about onset of arthritis of the hip, similar to arthritis affecting most people over 50.
SassyLassie also offered some good advice.
If you do consult with a chiropractor, find one who can also x-ray your hip, however MRIs are better in showing any hip damage from FAI.