I didn't eat/exercise very well when my dad died. I just stopped paying attention. You can come back from that, though, and it is important to take some time for yourself. But exercise can make you feel a lot better emotionally, so those walks are probably a great idea. Basically, you're already doing great for your situation since you're still noticing what you're doing during this time and haven't given up!
I got knocked down, but I got up again. They ain't never gonna keep me down.