I've seen 2 things that are similar to this: the first was in a pair of mature museum snakes, not mine (rosy boas) and it was a massive infection of some sort that
progressed from the tail, on up the spine of the snake (making bumps) before finally killing the snakes. They also had foul-smelling yellowish diarrhea. I forgot what
it was called, I recall looking it up though...not common, but not unheard of. I'm NOT saying this is what your snake has, btw.

The other similar thing is one of my large female FL rat snakes had an accident some years ago that damaged the tip of her tail, which had to be removed. Even though
the damaged part was surgically removed, she gradually got some tail bumps thereafter, which are not any sort of infection at all...more like arthritic changes. (they
stabilized, with no further progression, & nothing to do about it) So I can see why your vet first thought "infection" & then "trauma" as both are possibilities.

One afterthought about it being an infection: for the most part, snakes have solid pus, so that could be why your vet couldn't draw any out with a needle...but surely your
vet knows that? The inflammation would seem likely to engorge the area with blood too, which is what she withdrew, right? Does your snake have anything heavy in the
enclosure...like a large crock for water? King snakes love to burrow & your temps sound a bit too warm, so maybe your snake pushed her way under the water bowl to
cool off & her tail tip got stuck there long enough to cause trauma. That would be my best guess.

My rat snake did something similar, only it was the heavy cage top that sat on her tail too long & caused the damage; I was about to clean her cage...I unlatched the top
& went briefly to another room, never dreaming this silly snake would push up the top to escape...she wasn't known for pushing the top at all, but she did that time, and
she came all the way out but stopped with the lid still resting just on her tail tip! Like it didn't even hurt!? The resulting bumps in her tail were hard though, not soft
like you're describing. It sounds like your snake has some internal bleeding from trauma & hopefully it will all calm down & be OK.