Hi Donna,
Can you re-evaluate this dog from a TCM perspective? I take it the dog does not have Damp Heat as a cause of bleeding, given the formulas it is on, and the occurrence of bleeding despite that. So there are three other possiblities:
Qi not holding the Blood. The dog would have a weak or deep and wiry pulse, low appetite, fatigue, weakness, etc. Formula: Bu Zhong Yi Qi Tang. Points: BL 20, Sp 6, LV 13, GV 20, BL 15, BL 17, BL 18. Blood out of the nose would be watery
Blood stasis. The dog would have a wiry pulse, darkish tongue. Blood out of the nose would be dark or bright red. Formula: consider Xue Fu Zhu Yu Tang. Points: consider ST 37, 39; BL 17; BL 18
Blood Heat. Tongue would be red to dark red. Blood would be bright red. Dog may be heat intolerant. Pulse rapid deep and wiry. Points that would aid the pulse: GV3 or 4; GV 14; ST 36 (sedate); BL 17; LI 11. Formula: Qing Ying Tang.
In a case like this, where the diagnoses can be hard to differentiate, active points that change the pulse can really help figure the case out quickly. Qing Ying Tang is a blood moving formula, too, though and contains Huang Lian, which is an anti-leukemic. So if you've ruled out extreme deficiency, which should be pretty easy, then maybe just start with Qing Ying Tang.
Good luck!
Steve