Thank you for this info. Now I'm worried about two things: First and foremost, how any vet could just issue an antibiotic and send a bird with dark red hemorrhaging home. Please find another vet; another opinion. Blood this color is generally from high up in the intestinal tract and very often a serious concern. Too many things it 'could' be to list. Anything from a tumor/cancer, to other endocrine system issues.
What seems to be blood in the droppings might also be a type of bile. It could indicate anything from lead or other metal poisoning to the lesser seen, kidney infection.
Speaking of heavy metal toxicity: Have your vet perform a blood serum test for zinc levels (just in case your vet isn’t an avian-only vet, zinc levels over 2 ppm are positive for zinc toxicity). There will also likely be elevated WBC’s (white blood count).
Zinc can be ingested slowly over time when toys, clasps, chains, links or even cages are chewed on or played with. Other poisonings occur when the bird actually swallows a toy, link or piece of one. Watch out for bell clappers for instance.
X-rays should also be employed to rule out toxic ingestion like this. In fact, at the very least an Xray should have been suggested when this became "the second time".
I'm so sorry you're going through this frightening and frustrating time. The worst thing is not know what it is and thus, no idea how to make it better. Clearly you love this bird and are doing all the right things. I can't tell you how much I respect you for this.
My strongest suggestion at this point and given what's happening is see another avian-only vet quickly. If this actually is blood, birds can not just suffer from, but succumb to anemia relatively quickly. They just don't have that much blood in their aerodynamically perfect bodies to be able to tolerate much loss.
Please come back and let me know what happens ok? I'm happy to stand by you