Mazal tov on the birth of your baby!
We suggest performing a hefsek taharah and counting the clean days at your earliest opportunity. Once you complete the clean days, you need not perform any more bedikot and you can switch to colored undergarments to avoid becoming niddah from staining. (See more here.)
Please check in with your physician if a brief immersion in the mikveh (you could limit it to one dip) would be permissible once the scar is closed (usually by three weeks) and how to confirm that. You can prepare with a thorough shower rather than a bath. You could also arrange to be first in the mikveh after the water is treated to further reduce the chance of infection. If immersing under these circumstances is medically approved, then you could immerse to relax harchakot and allow for more physical closeness, even if relations are off the table until later.
We wish you a refuah sheleimah! Please let us know if we can be of further assistance.