Answer: Hirudo medicinalis, the European medicinal leech.
Today, leeches are not used for 'balancing humors' but instead to to reduce venous pooling of blood in delicate surgeries such as reconstructive and reattachment surgeries. Medicinal leeches secrete a number of anticoagulants in addition to hirudin which facilitate blood flow and therefore promote wound healing.
Note that leeches are annelids and not trematodes, despite their superficial resemblence. You can appreciated their segmented nature in this photograph:
Medicinal leeches carry Aeromonas hydrophila in their gut. Therefore, it is important to give the patient antimicrobial prophylaxis when prescribing medicinal leech therapy.