What tests should be done for low back pain? Do I need MRI, CT and blood tests?

Generally speaking, there is no need for tests. If the doctor thinks there is nothing serious through consultation and examination, he/she will suggest conservative treatment first by exercising the strength of the back muscles, and if this does not relieve the pain, it is not too late for further tests.
If you are still unsure, you can take a frontal and lateral x-ray of the lumbar spine to see if there are signs of fracture dislocation or slipped lumbar spine, lumbar spinal stenosis and narrowing of the lateral saphenous fossa, narrowing of the intervertebral space, etc. If there are no such signs, and if the patient’s examination and physical examination do not show any clear signs of nerve damage or destruction of vertebral bone and disc, further MRI and CT examinations are not required. If vertebral bone destruction and intervertebral space destruction are suspected and there are clear signs of nerve loss on examination, MRI and CT should be done. If abdominal problems are suspected, an ultrasound of the abdominal organs should be done.