Mazal tov on the recent birth of your baby!
As long as you did not actually see the pink thread of blood exit your body, stains found on the shower floor or on the bathtub may be disregarded and do not invalidate your clean days.
You may continue with your original count of the seven clean days. If you continue to experience staining, you should change your white underwear more frequently to prevent stains from accumulating to a gris (the size of a US dime or Israeli shekel). Stains smaller than a gris on your underwear may be disregarded. You may also reduce the number of bedikot required to one per day if the staining continues. Finally, be sure to bring any questionable stain to a rabbi for evaluation, since not all stains will invalidate the clean days.
We understand that you were alarmed at seeing the stain, and wanted to confirm that you weren't bleeding. However, it is not halachically recommended to perform a bedikah in this situation. If a stain invalidates your clean days, a clean bedikah will not "undo" it. And if a stain does not invalidate them (e.g., because it is too small), you risk invalidating them if you find blood on the bedikah.
Please feel free to get back to us with any further questions.
B'Hatzlacha!