That really does sound nasty...if it helps though, I had a tooth extracted once and the post-care leaflets said that if there was bleeding to make sure you swallowed it and that you must not spit it out as that would make it carry on bleeding for longer (no idea how that works but that is what it said)

I'm sure it wouldn't make you vomit, it's just the thought of the fact that it is blood, but your stomach has no idea with what things are, it just digests them, iykwim? Like I'm sure if I knowingly ate something icky like offal I'd feel very sick but if I didn't know what it was then I wouldn't.

Get well soon