I think a good friend could have seen you were flustered and mortified, basically you were trying to get the poo-covered child out of her house (as she still had poo on her clothes) and personally I think that was the best thing to do.
If they know you have social anxiety, a bit of slack can be cut. My child recently was sick in a well-known restaurant chain, and they were sooooo nice about it. These things happen, and yes, we did rather flee (after offering to clean up) through embarrassment.
I don't think you necessarily handled it well, but your anxiety shines through and personally, clearing up a bit of sick and poo would be nothing to me, I'd be more interested in trying to make my guest not feel bad, I would even have left the bleaching til after they had gone and the child was in non pooey clothes.
I think people have been overly harsh on you here, good friends would have helped you get out of the door first, and wouldn't text you saying they are angry and not coming round your house next week. At most, they might have said they were surprised you rushed off (with a poo-covered child?)