Hello and welcome to the forum. Thanks for question and we hope you find the information helpful. The best source of information is to speak with the doctor that performed the cauterization. They can guide you in terms of whether this is normal post operative recovery or a complication and what your next steps may be. The procedure you had is likely radiofrequency denervation as the technical term. It can be effective for neck pain if it is not caused by disc or other issues in the back which are also common causes of back pain. Here is a link: https://www.webmd.com/arthritis/radiofrequency-ablation#1
Numbness is usually supposed to be temporary. Four weeks seems like a bit too long but every person is different. Please speak to your doctor about this for follow up. There are complications can occur and we hope this isn't the case for you.
Please let us know what your doctor says.
I had that done the end of March 2019. Radiofrequency. My MD told me my pain would get worse before it got better. 4-6 weeks & it took all of that. At my follow up I told him it was pure hell & I now know why they don't want to see you for 6 weeks.
My pain is better except for the C-5 and C-6 area where I have a tarlov cyst and damaged spinal nerve root.
I feel your pain, Physical Therapy has helped but you need to find someone who does myofascial release. Also cranial massage.