I have had a lot of experience in dealing with depression and can attest that stress (regardless of the source) is the single worst thing for it. I also have a younger brother that experienced the exact shutdown response in school when he was younger, and he was later diagnosed as dyslexic.

As far as answering your final question, exercise and getting outside is more effective than anything else from personal experience. For those out there who struggle with physical limitations due to health issues (also have experience), a good coping mechanism can be to set aside time purposefully each day to reduce your sensory inputs while practicing deep breathing or stretching. One final note is that diet plays a significant role in the body's ability to process stress. There are many testimonials from people that a ketogenic or carnivore diet (at least followed as closely as one reasonably can given their circumstances) does help depression/panic due to the stabilization of insulin in the body thanks to not consuming as much sugar. Of course, this is actively suppressed by large media outlets and public health (they have their reasons), but that's a separate discussion entirely.