Welcome To Ask The Doctor.
The pain you are describing seems to be of Prolapsed Intervertebral Disc (PIVD).
In fact when we examine a patient with low back pain we do this test called as Straight Leg Rising Test. If a person has pain on passively raising the straight leg, it is suggestive of PIVD.
I would advise in such scenario to get a MRI of Lumbo sacral spine done.
The treatment would be based on the severity. If the nerve compression is not severe, you will be treated with Pregabalin, Methylcobalamine, Duloxetine, Physiotherapy.
I hope the information helps.
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