Edit: to give a fictional character his due, he's a Welsh monk who lives in England, not an English monk.
Hello, I wrote an answer here about 9th century medicine and pharmacology which is still broadly relevant to the C12th.
The tl;dr is that yes, even if medieval medicine doesn't quite match up to modern standards, a lot of its cures and treatments are based on real, observable science, and a lot of modern medicines are essentially just the refined versions of 'herbal' remedies. Bald's Leechbook, for example, prescribes wormwood tinctures for a variety of fevers and illnesses; wormwood is used today as a source of artemisinin - commonly used as a rapid response to malarial fevers - as well as an antihelminthic, a drug used to expel worms and parasites from the body.