Training is bare foot, and work is a female version of a typical 'workman's boot' with steel toe caps (don't ask why!). I've put comfortable soles in them and they are actually very supportive and comfortable.
There is a current thought, with regard to running and footwear, that less is more. We have embraced these heavily cushioned running shoes with lots of support and stablizers and whatnot, and it can actually lead to more foot injuries. The cushioning causes you to actually strike harder when you run, and the arch support undermines the very design of an arch, which only works properly if there is nothing under it. The foot, in it's design, is meant to work naturally, and when we wrap them up in thick shoes with lots of cushioning and support, we are preventing the foot from functioning in the way it is meant to. This causes the foot to get weaker over time because it doesn't do any work anymore. Think about if you break your foot and wrap it up in a cast for six weeks, the muscles of the foot and leg atrophy. After the cast comes off, you need to rebuild that strength again. This is kinda what happens every day when you put thick padded shoes on your feet. Over time, as the feet get weaker, they become more prone to injury. People try to solve the problem with MORE cushioning and support, which just makes it worse.
The solution, among runners, is a return to a more minimalist running shoe. Shoes that are more like a thin slipper, with a thin sole and no cushioning and little or no support. This allows the foot to function more naturally. It also require that you re-learn how to run because you need to adjust your stride, shorten it, make for a mid-foot strike instead of heel strike, and a certain gliding stride that lessens the impact. It takes a bit to figure it out, but it works. It also requires time to allow the feet to regain their strength before one can run very far again, but it brings the function of the feet back into the running action, and is better for us.
This is how people used to run prior to about 1970. That's when Nike began making modern, cushioned running shoes, which changed how people run and basically destroyed runners in the process.
This may have something to do with what is happening to your feet. It might be that your shoes are too thick and give you too much cushioning and support, and your feet are simply getting weak and prone to more injury. Switching to a thinner shoe that allowes you to feel the ground thru the soles of the shoes might help you regain the strength in your feet and these problems might go away. Whenever you can, like when you are at home, being bare-foot or just with socks all the time might help to begin rebuilding this foot strength as well. Just take the shoes off whenever possible. Stretch and flex your feet and just keep walking around the house, barefoot.
I would suggest a visit with a podiatrist first, to make sure you don't have any serious injury to your feet that require treatment. But then going a more "natural" route with the shoes and the feet might help.
A good source of info on this is the book Born to Run, by Christopher McDougal. It's really about runners and people who run super long distances, like 100 mile races and stuff, but he talks about the shoe issue and it's a fascinating book.
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