Can ovarian cysts cause a shooting, stinging pain down the thighs? Should I be concerned? Low ab pain (sore) pelvic pain (gas-like)

They can. Cysts can cause different sorts of pain. They cause pain from their size, from twisting around or fro bursting open. They can cause nausea or GI symptoms as well. So if the pain persists, you should be evaluated for lots of sources.