All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
Since you are not sure that some blood came out, then you do not have to cleanse your mouth, but if you are certain of that, then if this blood was little and a pardonable amount, then it is not an obligation to remove it.
In any case, your ablution was valid even if we presume that there was some blood on the inside of your lip. Rinsing your mouth is sufficient to remove the impurity, if we presume that there was any, and it is sufficient instead of the legislated rinsing of the mouth.
The author of Kash-shaaf Al-Qinaa' said, “If a person intends to remove the impurity along with the intention of performing ablution, then this does not affect the intention.”
We remind you here that it is not permissible to swallow blood, so if you find its taste in your mouth, you must spit it out because it is impure and it is not permissible to swallow it.
Allah knows best.