I started walking around the house the second week as well. I did not start working out until 2 months pp.
The first 4-6 weeks, I spent doing deep core exercises. It doesn't seem like doing much by doing these, but it was to start activating the core and all ab muscles. I'm talking about the exercises that are meant to fuse both muscles up if it parted. Mine didn't part but it's supposed to help with your core.
After that was done, I started a workout regimen by 2 months pp. a 3 days a week program of beginners mode. If you have worked out pretty consistently before pregnancy, you're considered a beginner again after pregnancy, especially after c/s. So I did squats only for lower body with a 1lb dumbbell each hand, as you wanna start out as low, very very low. Do not f around with your post section recovery! Depending on how you feel, I highly advise to start very low and baby steps. So anyway, for upper body, I did overhead press and other typical upper body exercises.
I'm now at 4, going on 5 months pp. Just take it easy. Listen to your body. When I go to hard, even now, my scar tend to tingle or get sore, so I'd stop. Most are so eager to start working out. I recommend to activate you tva first. Google it, you'll see how to. Or YouTube it.