She thought he had banged his nose on the wall because she had been careful to whack his butt even though she was mad. As a rule, frothy red blood comes from the lungs. The vessels in the lungs rupture under exercise and the horse sometimes bleeds enough to have it come out. She also said there is no consistency as to the length of time he'll go while working before he balks. It's possible he goes until the discomfort in his lungs becomes too great to keep going freely.
Aggression can have a physical cause as well as a fear and disrespect cause.
If a horse is in pain, it will not want to work or cooperate any better than a human will under pain. His attitude seemed somewhat better after the bonder but not anywhere near what i would have expected. When he came back into the pen for an under saddle exam I immediately noticed a weird dip in his lumbar region. Upon closer examination I noticed he had several lumbar vertebrae out of position. I noticed he had a number of cervical vertebrae out as well.