Mazal tov on the birth of your son!
A regular gynecological exam does not usually render a woman niddah, since only uterine bleeding renders a woman niddah. However, since non-uterine bleeding can result from an examination, be sure to ask your physician if anything she is doing might cause bleeding, why, and from where. See our article on speculum and manual exams for more information.
Even bleeding that does not render you niddah can complicate the clean days, when you wear whites and perform bedikot. To simplify matters, you might consider delaying your appointment until the day after mikveh immersion. If you do not change the date, just be sure to perform your bedikah (if possible, both of them) prior to the appointment. If the appointment is before the late afternoon, then you may omit your second bedikah. Even if there is any staining prior to mikveh, if it is consistent with the doctor’s explanation, then you may immerse.
With regards to contraception, it is best to consult with a rabbi with whom you have a personal relationship. If you would like a ruling from our site’s rabbi, Rav Yehuda Henkin, please write back with details about your children and their ages and any other information you think should be relevant.
In choosing what method of birth control to pursue, you would consult your physician for the best medical options and then get back to the rabbi who granted you the ruling.