All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Rinsing the mouth is an act of the Sunnah according to the majority of scholars. The saying that it is obligatory is restricted to when the person is capable of rinsing his mouth, because the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said: “If I command you to do something, do whatever you can thereof; and if I forbid you from doing something, then leave it.” [Muslim and others]
Consequently, there is no harm if you do not rinse your mouth as long as this causes your mouth to bleed.