Welcome to the board. You have my sympathy for the reason that you found us.
Two things struck me about your post. The first is that your doctor is already talking about surgery after only 10 weeks' time, and two, the diachotomy between what you've been told is clearly S1 symptomology and the herniated L4 disc.
Disc pain from a herniation can cause a variety of sensations and nerve pain. The dermatome charts are a generalization and not specific to each and every human being.
Herniated discs can and do heal on their own. My husband ruptured a disc about 15 years ago in his lumbar spine. I served him Christmas dinner on the floor as he could not sit in any chair. Two different spinal specialists advised that he was not a candidate for surgery at that time, and that he would heal on his own. To this day he takes good care of himself, does his back exercises faithfully every morning and has not had any further problems.
I on the other hand had a PLIF at L4-5 in January and am in the process of recovering. I had sciatic pain for about 3 years before I finally decided to give up and have the fusion.
Most doctors are reluctant to do surgery without exhausting all other options unless there is bowel or bladder involvement, in which case surgery is done immediately.
If I were you, I would explore other options before thinking about surgery. I would also get at least another opinion from a fellowship-trained spinal specialist. I would see a neurosurgeon and also an orthopedic surgeon, both who only see spinal patients. I found there was quite a drastic difference in what each was suggesting.
Do not make the mistake of thinking that surgery will restore you to the way you were prior to the injury. It may or may not improve your pain, but it will not make you whole.
Feel free to ask questions and read everything you can about your situation.