Had back pain now leg pain i get bad pain in my right leg when i cough had it for three weeks now?

Sciatica: It sounds like sciatica. Get a doctor to examine you and do a neurological examination. He or she may also order radiological study for more accurate definition of your sciatica. Best wishes.

Herniated Disk: Sneezing and coughing resulting in back pain is a typical finding in someone with a herniated disk. If it does not resolve on its own in a few weeks, i would see your doctor to evaluate the spine further with imaging studies.