Could a burning sensation on the left side of my head be a stroke symptom?
The fact that this sensation only comes on with anxiety and stress makes it most likely a benign headache type, such as a migraine or migraine variant.
That said, if it is the first time anything like this has happened to you, I would err on the side of caution and talk to your doctor about obtaining an image of the brain, just to be sure there is no anatomical reason for the sensation. Either a CT scan or an MRI should be fine. A big element of how aggressive to be in evaluating this pain is your age and other risk factors. If you are young and otherwise healthy, this is most likely a benign issue. If you are older and have other health problems, I would be somewhat more aggressive about getting a good quality image of your head and brain.