A 2003 systematic review [1] looked at sympathectomy for facial blushing and the authors concluded:
We did not identify any controlled trials or cohort studies. The evidence about effectiveness, based on three case series, was therefore very limited. The main weakness of these studies was their lack of a comparison group and their resulting inability to exclude a placebo response to surgery. In addition, the methods of assessing outcome were poorly described and not validated, and the range of outcomes assessed was limited. The studies provided very limited evidence that sympathectomy improves blushing. Side effects were common.
A 2007 systematic review [2] of endoscopic thoracic sympathectomy for excessive sweating and facial blushing concluded:
The evidence of the effectiveness of ETS is weak due to a lack of randomized trials. The intervention leads to severe immediate complications in some of the patients, and to persistent side-effects for many of the patients.