A CT scan will not show the nerves or if they are compressed. It will show how much room there is for the nerves to pass through the areas of the foramen of the vertebrae.
MRI scans are done to see if there is nerve compression.
I would think that your doctor would have ordered an MRI to determine if there is nerve compression.
Your research is correct about conservative treatment and it is possible that another doctor would say the same thing as your present one is saying.
On the other hand, you could get very different opinions as well, and it's important to have more than one opinion, especially when you are not comfortable with the doctor or the doctor's advise.
My concern for you is that your present doctor is ignoring you, what you are telling him you are feeling and where your pain is.
A good doctor will be listening to his/her patient and what the patient is saying, where the pain is located and what the patient is feeling.
x-rays, CT scans, MRI scans are only tools to use in the diagnosis of a patient, and they should be used only as a guide to help the doctor match the symptoms that the patient is experiencing and finding the cause.
From what you are saying, your doctor is using the x-ray pictures only to diagnose you and is not listening to you.
The x-ray pictures diagnose a specific spinal problem, but it is not explaining why you are in the pain you are in.
You should try and explain to your mother that you understand that she thinks any other doctor would say the same thing, but your doctor is not listening to you and is not suggesting the appropriate treatment for your known spinal condition. Your doctor is not using the usual protocol to treat you and the best thing you could do is get a second opinion before fully following the advise of your doctor.
You should tell her that you are not comfortable with your present doctor, he doesn't listen to you, doesn't seem to care what your symptoms are and doesn't remember things that you told him, including the pain you are in.
Those are all signs of a doctor that is not doing his job, is not treating you properly, doesn't respect his/her patients and you need to seek out a second opinion and do it right away.
Good luck and keep us posted on how things go.
Fran