Usually not, but there might be species that are resistant to their own venom. Venom is usually stored in a way that it does not enter their blood stream or go elsewhere in the body that it could cause damage. Some poisonous plants do something similar, where the toxins are not active until cells are ruptured, after which the inactivated form of the toxin has an enzyme cleave off what makes it inactive and what is left is the toxin itself.
The human body itself does something similar in the pancreas, it’s not venom but loose pancreatic enzymes would dissolve your organs if they weren’t contained. Pancreatitis where those enzymes get released in the pancreas itself causes the pancreas to start digesting itself, and is life threatening.
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