Mazal tov on the birth of your baby!
Based on your description, you may well have some sort of cut or lesion in the vaginal area. If the spots are in the same place on the bedikah cloth every time, then this is almost certainly the case.
Blood from a cut or other trauma is not uterine and so does not make a woman niddah or invalidate her clean days. If it is established that you have this type of non-niddah source of blood, then it will not invalidate your bedikot or clean days. However, a hefsek taharah needs to be free of red blood.
We recommend that you have the area checked to see if you have a lesion. This can be done by a physician who can also see if any treatment is necessary. For dealing with the halachic issue only, it is possible to see a bodeket taharah, or niddah nurse, who can establish if this is the case and also help you get a clean hefsek taharah. If you'd like to share your location with us, we can attempt to make an appropriate referral for a bodeket.
Please write back with any further questions.