Mazal tov on the birth of your baby!
It can be challenging to return to hilchot niddah in cases such as yours, where there has not been much time to gain experience.
A woman is not required to perform bedikot outside of the designated days, and it is usually not advised without prior consultation with a halachic authority.
When a woman has staining that does not make her niddah, she is strictly speaking permitted to have relations. In such cases, we usually advise abstaining from relations for twenty-four hours, by which time staining has often ended or developed into a flow. This is a precaution against having a flow begin during relations, but not a halachic requirement. In your case, there is the additional possible lenient factor of the cervical tear.
Based on what you write, you understood yourself to be possibly spotting but not in niddah when you had relations. In such a case, we would have advised abstention as above, but would not consider you to have violated halacha.
It is important to note that there is a range of opinions on the niddah status of a woman who sees spotting on toilet paper. For more information in evaluating what you saw on paper, please see our site's article "Toilet Paper." Then please reply with any follow up questions.