Coughing and vomiting blood, no matter how severe, will only cause "spatters" of blood on the floor. This is not enough to contaminate anything else.
If you use a bleeding symptom, then it's possible to create pools of blood, which will then get tracked onto any passersby.
However, this still doesn't change the main problem, which is the fact that ENTERS_BLOOD toxins don't change the afflicted creature's blood to carry the toxin independently. Only the original source can spread the disease.
It is possible to make dwarves that have blood that is poisonous to dwarves. What this does is it makes the dwarf wander around just fine and dandy, until he gets hurt by something and bleeds on himself. Then he will start displaying symptoms. If he bleeds on anyone else, they will also get infected.
If this happens to be a disease that causes bleeding, you'll end up with an utter mess after a while...
As for insanity, nope. No personality or behavior altering symptoms are available. We've got puking, blisters, swelling, pain, necrosis and a lot of other fun physical ailments... But no dementia or other neurological goodies.
Also, this eye-popping thing sounds a bit... Odd. I can imagine massive bleeding, but unless there's something special hidden quirk to the swelling or bleeding symptom tags, then I can't imagine how it would be possible. You wouldn't happen to have a link to that thread, would you?