Mazal tov on the birth of your baby!
Staining of duration such as you describe happens to about forty percent of women taking a low-dose combination pill. Over half of the women who spot during the first month of pill use don't spot in the second month. In the meantime, there are steps that you can take to help assure that you get to the mikveh as soon as possible.
Staining does not necessarily invalidate the clean days. We recommend making an attempt at a hefsek taharah. The hefsek taharah need not be completely clear, so browns should be brought to a rav for evaluation. In this situation, the moch dachuk may be omitted and you may perform only one bedikah per day.
Any questionable bedikah cloths should be brought to a rav for evaluation. Stains on undergarments should also be evaluated. If the stain is light brown with no hint of red or if the stain is smaller in area than a gris (roughly, the area of an American dime or Israeli shekel), then it does not invalidate the clean days. Changing undergarments more frequently than usual may help keep stains larger than a gris from accumulating. If these measures are insufficient, please contact us or a local rabbi.
If the staining persists beyond the next month or so and cannot be managed with the above advice, you can contact your doctor about switching pills. While breastfeeding is best for infants and should be continued as long as desired by mother and baby, by thirteen months an infant is usually not entirely dependent on his mother's milk. As such, taking a slightly higher dose pill would not be out of the question. Use of combined oral contraceptives during breastfeeding is permitted by the American Academy of Pediatrics. The main concern is that higher dose may reduce the milk supply. However, at this age, even if the milk supply is temporarily decreased, your baby should still be able to get proper nourishment from solid food.
We hope the above helps. Please get back to us with any further questions.