I had always been a limber kid and could put my foot behind my head and other funky stuff. I could (and still can) make my hips come out of joint (I don't do it intentionally NOW, whereas when I was a kid I did it to gross people out). This has caused me hip pain, sometimes to the extent where pain shoots down the leg, mostly down the back side.
The shooting pain is most likely the sciatic nerve being pinched somewhere in the hip. This MAY be a misalignment which can be adjusted by a chiro. I lifted some really heavy stuff a couple years ago and had to have my chiro YANK on my leg and twist to get it back in the right spot. Now THAT was fun.
If possible, have the hip joint x-rayed. That may show if anything is pressing against the nerve. If not, then a cat scan or mri would be better but is much more expensive. Great if you have insurance, although you wait for authorizations.
Arthritic pain (and I am very NEW to this) is more of a constant pain and/or stiffness. The shooting pain you described I believe is most definitely a NERVE pain.