Yes Inchworms do have brains.
All worms including Inchworms have brains and the Inchworms and other worms brains connect with nerves from their skin and muscles.
The Inchworms nerves that connect to the brain detect light, vibrations, and even some tastes, and the muscles of their bodies.
Just like humans and other animals the Inchworms and other worms breathe air but unlike humans and other animals the Inchworms do not have any lungs.
The brains that Inchworms have is different than human brains though but they do have brains.
The brain in the Inchworm is also tiny and is connected differently than humans brains or other animals brains.