I had exactly the same problem, but in my case it was my left thumb. Treatment was in 2001, using a private heath provider (BUPA), when I was working back in the UK. Treatment was surgery to remove the disc. This required access to the spine through the front of my neck, the surgeon's incision was along one of the creases in my neck and is barely visible. The incision was on my left side, in your case probably the right. A piece of bone was taken from my hip and inserted between the vertebrae, resulting in fusion of the bones (cervical fusion). The most painful aspect was the removal of the piece of bone from my hip, the neck didn't hurt at all.
My experience may be different to other sufferers, and was 25 years ago, so things have moved on with 3D printing and so on. Even in 2001 there were different methods, some surgeons used bone from the hip, some didn't use bone at all.
The operation took about four hours and I spent 10 days in hospital. I had to wear a rigid plastic collar, to imobilise the neck and head, for three months, even in bed; I had to sleep propped up. I could shower, which meant removing the collar for a short period, but very carefully! Rotation of the head from side-to-side becomes restricted because two vertebrae are now fused. I was warned that would put extra stress on the remaining discs, so needed to be aware of this.
Following the stay in hospital I had pain in my shoulder and left arm, traction was prescribed, which entailed having a 'noose' fitted around my neck and under my chin with a strap taken over a pulley behind my head and weights added to stretch my neck. This worked after a few weeks of treatment.
Over the years I have had associated 'pain', more discomfort really, and have taken pain killers since, but only when needed. About eight years ago I had problems with some pain and discomfort and had to have an injection through the side of my neck to an area close to my spine, I was able to watch the needle via an X-ray monitor, there was no pain or discomfort, and it was fascinating to watch! And it worked.
Ever since the operation my arm has been numb along the line of the nerve from my thumb to my shoulder. This isn't really a major problem, the lack of feeling in my thumb sometimes results in me dropping things, thinking I have a good grasp but don't. The upside is I haven't felt an injection in my arm since! The numbness is only along the line of the nerve, the rest of the arm is fine.
The numbness is due to the nerve being damaged by the pressure from the ruptured disc, so surgery is essential if this is to be avoided. I recommend that you don't waste time. Hope this helps.