No. The bowfin (Amia calva), also called mudfish or choupique, is not poisonous or venomous. It has no venom spines or toxic glands, and its only defense is a large mouth with small, sharp teeth, so handle a hooked one carefully to avoid a bite.
Bowfin are also safe to eat. The Florida Fish and Wildlife Conservation Commission notes that the flesh is soft and jelly-like but can be smoked, fried as patties, or stewed. As with any freshwater fish, check local consumption advisories for the specific lake or river where it was caught.
Source: Florida Fish and Wildlife Conservation Commission: Bowfin
Image: Amia calva, Milford, Virginia, by Brian Gratwicke, CC BY 4.0, via Wikimedia Commons.