I also have atypical TN on both sides. It started on the right side after I had gotten the Flu vaccine 10 years ago, I was 38 years old. It has been controlled with 200 mg of Topamax daily. Last year I had come in contact with the Flu virus once again and I developed TN in the left side. This time it was unrelenting and the pain would not stop. I was desperate to make it stop. No matter how much medication I took, it wouldn't touch it. I decided on a rhizotomy. I must tell you that it is not without risks. I woke up in more pain than I started and suffered a minor stroke 2 weeks after. I still can feel pain on the left side of my face. And I do get some tingly numbness. I would definitely NOT recommend the surgery. I would not do it again for my right side. I rather stay on meds.
I have TN and have had a successful rhizotomy. However my TN is related to MS. Looking on the various TN websites regarding atypical TN, I do not see many comments about atypical being helped by rhizotomy. You may want to do some research on google scholar which lists scientific articles or on sites like facial pain org or living with TN com
Perhaps another member of our community will have more info for you.
Let us know what you decide and how you're doing