[Routine Help] Layers of dead skin after years of poor hygiene

Hello, throwaway because this is incredibly embarrassing, gross, and I'm ashamed. I'm sorry if this kind of post isn't meant for this sub. Gross warning.

Recently, I've been coming out of a multiple year-long depressive episode where my hygiene drastically fell. To the point where I was only showering once a month, unless I had to leave my house for whatever reason. Now that I'm starting to take better care of myself, I'm struggling to fix the aftermath of the dead skin that has seemingly built up on my body. My feet, legs, and arms seem to be suffering the most

No matter how much I scrub, I can't seem to remove these layers. An example of what I mean: If I get in the shower and allow my legs to soak up the water for a bit and then run my nails up my legs, my hand will come away with layers of dead skin stuck under my nails. My legs will then be left with visible flakes of dead skin that still need to come off. No amount of scrubbing seems to help, more flakes will just appear. I get the same results if I exfoliate with a (admittedly, 5+ year old) sugar scrub, and then do the nail thing. Still layers of dead skin under my nails, with visible leftovers on my legs that seem to be never-ending. Rubbing myself dry afterwords makes it much worse as well

I can only imagine this is the result from years of build up. I can't seem to figure out a good routine/products to use to finally scrub off these layers. I feel gross getting out of the shower, knowing and seeing the dead skin but unable to do anything about it

TL;DR: Please help me figure out a routine and products to clear away the dead skin from my legs/feet/arms, and just whole body in general. Even before my depression was at full power, I wasn't knowledgeable about skincare, so I'm super lost about where to start. Note: I do not have a tub and am unable to do anything that requires soaking in a bath. Thank you for your time