I'll tell you a quick story about my feet, and how changing the shoes fixed arch pain I was having. My job is different then yours, I walk quite a bit but also sit alot, but one day my foot arches started aching like crazy for the first time in my life. Like you it was aching even at home when I was relaxing. I never had foot problem ever and finally realized I had changed to new shoes about a week before this. I would have never guessed just a shoe change would cause so many problems but it can creep up on you without you even knowing. I ended up getting jogging shoes, and its made a world of difference. I dont mean the jogging shoes you buy online that are from china, I mean go to a jogging / running store, and buy the really good running shoes. They are different, they last longer, and they have a "spongy" feel when walking. I paid roughly $170 for them, these aren't the $45 running shoes you find online. They actually had me stand on something to check foot pressure, then a digital screen showed where your pressure is when you stand, then they match the shoes for you.
Like I said my job is different then yours, but no doubt in my mind the shoes can change everything. Even when I walk on treadmill I no longer wear any shoes except specialized running shoes now, and I havent had any arch pain since I started doing that. Take care of your feet.