Of course we are all different and our symptoms and experiences can differ, but i will tell you my experience. I was diagnosed in 92, I think. I was able to get by on medications for quite a few years though the meds had bad side effects. When the side effects got too bad and the pain was not contained by the meds, I tried various outpatient surgeries. Radio frequency Rhizotomy worked fine for almost 4 years but my face was very numb and it threw my bite off. When the pain came back, I used meds again till the pain escalated again. Then I tried a balloon procedure that only worked for a few weeks. Finally I had the big surgery - Microvascular Decompression. I would probably have been better off if I'd done that years ago. It took all the pain away, allowed me to get off all meds. I think recovery took maybe a week. I had some bad headaches after it and took some pain meds for the pain from the surgery, but it was well worth it.
I think for most people the pain gets worse over time. But I know some people whose pain went away. It makes sense to me to try meds but if the side effects are bad or they don't help enough, surgery can be a lot better. I guess COPD could make surgery a more difficult choice. A neurologist can help you make the decision.
Good luck and I hope you find what is best for you!