How do I relieve the pain of severe sciatica caused by a herniated disc?

Spine Pain Options. This chronic pain in the distribution as you suggested is the result of an irritated nerve or facet joints or other injury typically in the lumbar spine (low back) which are caused by herniated disks, spinal stenosis or degenerative disc disease, etc requiring further evaluation by a spine specialist and may be candidate for facet injections/radiofrequency ablation and epidural steroid injection.
Some ideas. Herniation is usually the result of either trauma or misalignment of spine (subtle or major). Try omt from osteopathic physician (aao or cranial academy online). See your doctor for short term pain relief - then go after the cause as this usually recurs over time. Long term: omt, slow yoga, feldenkrais, alexander technique, bowen ; other bodywork or pt along w/ core strengthening-after alignment.
Medication rest . You can try reclining or lying down in a fetal position and take Ibuprofen or Naproxen ( if no Aspirin allergy or GI issues or concomitant use of blood thinners) along with tylenol (acetaminophen). Otherwise see your physician to see if a Medrol dose pack may be warranted which is a tapering dose of steroid medication which is a potent anti inflammatory. An epidural steroid injection can also be of help.