While there are some physical responses to stress, for clinical purposes best practice is to simply ask the patient regularly how they are feeling, and to keep a log of stressful events in their life.
One thing I found helpful is an app called Migraine Log. I don't have migraines, I just use it to track how I'm generally feeling. I set up a reminder on my phone, every day at 9 PM. The app is great, it lets you rate each day on a simple scale of green, amber, or red, and optionally add a note. All data stored locally, open source, no internet permission at all.
Smart watches, bands, and rings are quite good at some stuff. The high end ones have pretty accurate heart rate sensors, on a par with medical devices like chest straps, and the very best like the Google Watch can take that data and use it to do a decent analysis of your sleep cycles. The cheaper ones are mostly just okay, giving a decent indication of heart rate and overall activity levels, but things like sleep tracking are little more than random number generators.