Toe hyperextension when I walk

I’ve been working my way through the CHOP protocol for POTS and have been walking/almost jogging recently. I’m having issues because of hypermobility in my toes (and maybe my feet more broadly, but definitely my toes) … I’m not sure if it’s a shoe issue or the way I’m walking or what. I did figure out pretty quickly that I was walking wrong and had to teach myself to walk “correctly” with the help of YouTube, and overall, things are much less painful, but my feet start to hurt pretty quickly; it feels like my toes are hyperextending. This is not new — I regularly injure my big toes by hyperextending them when I’m barefoot or in flip flops, although I am wearing sturdy sneakers when I walk on the treadmill. Is this something to correct through how I walk, or should I look at braces or different shoes — and if so, what should I look for in braces or shoes?

Any tips would be appreciated.