Mazal tov on the recent birth of your baby!
You may slightly moisten the bedikah cloth with water to help alleviate discomfort during a bedikah. Be sure to go gently and slowly while performing the bedikah. You can also try lying down while performing the bedikah to see if that is a more comfortable position. If you still experience discomfort despite these steps, you may lubricate the vaginal area (with KY jelly or similar water based lubricant), wait 15 minutes, and then perform the bedikah.
Additionally, in extenuating circumstances such as these, one may reduce the number of bedikot required. You should perform the hefsek taharah (omitting the moch dachuk) and one bedikah daily during the seven clean days. If even that is too painful or uncomfortable, you may reduce to the hefsek taharah, and one bedikah each on days 1, 7, and one additional intermediate clean day.
Please feel free to get back to us with any further questions.
B'Hatzlacha!