Blood going down the throat unknowingly

My gums are sensitive and bleed when I brush my teeth. I try to not swallow when my gums are bleeding however some saliva goes to my throat and since, short of actually throwing up, it would be quite difficult to get that back up and out, I end up swallowing whatever escapes to my throat. Also, my gums tend to continue bleeding (very lightly) for hours afterwards and not swallowing at all for that long seems near impossible. I don't swallow whatever remains in my mouth, and I try to not let it go to my throat. Am I sinning?