Can endometriosis cause shooting pain from the left side of the belly button down to the vagina?

Yes. Your pain may be due to your diagnosis but only a complete evaluation will prevent missing something more serious.
Endo pain. That type of pain could be due to endo but could be due to bladder or pelvic floor muscle spasms or even bowel.

Related Questions

What to do if endometriosis causes shooting pain belly button in the vagina?

Hormones or surgery. Hormones may control this pain, but you might need a surgery to eliminate as much disease as is seen or to remove adhesions.

What causes shooting pain in belly button and vagina during and after urination?

Possible UTI. Urinary tract infections (uti), either of bladder or kidneys, are described as painful frequent urgent urination. Bladder infections have symptoms localized to the pelvic region. Kidney infections may include back/flank pain plus fever/sweats/chills. Go see your family physician and get evaluated. If indeed you have a uti, antibiotics are only solution.