Mazal tov on the birth of your baby!
Post-partum bleeding tends to come and go in waves, so renewed uterine bleeding is a real possibility. However, especially given the bright red color, bleeding from a wound (like an episiotomy, or tearing, or hemorrhoids) is also a real possibility.
Even when there is no wound, a woman is not always considered niddah after she finds blood on toilet paper. For example, if you follow sephardic halachic rulings, or if an interval of at least a few seconds passed between urinating and wiping, you are not considered niddah. (For this reason, we recommend that women deliberately wait, ideally about fifteen seconds, between urinating and wiping.) For a discussion of the factors involved, please see our site’s article “Toilet Paper.”
Additionally, blood from a wound, dam makkah, does not make a woman niddah. To determine if your blood can be attributed to a wound, you can try looking in the mirror to see if you can identify any irritation or lesion that looks like it might bleed. Or you can see a niddah nurse or bodeket taharah, or your physician, for an examination. If you or they can identify a non-uterine source of the bleeding, we can consider what you found on the toilet paper to have been dam makkah.
If you determine that you are in niddah, the usual rules of becoming tehorah apply, even though you immersed just a few days ago. Keep in mind that this is likely a short-term issue. Once post-partum bleeding ceases, many women experience months without a period.
Please write back with any follow up questions.
This response has been updated to reflect the rulings of our current Rabbinic Supervisor, Rav Kenneth Auman, regarding waiting before wiping.