You may sue your neighbour. Owners of pets or persons in charge of taking care of pets may be held liable for injuries caused by their pets. Depending on which state you live, there are some legal concepts that may apply to put legal liability on the person responsible for an animal that harmed you.
First, the snake may be considered a “wild animal”, a group that includes lions, bears, wolves, sharks, among others. Persons who are keeping wild animals as pets are strictly liable to the person harmed by the animal.
Your neighbour’s snake may also qualify as an animal with a “dangerous propensity,” or animals known for their violent and vicious tendencies. If owners have been proven to have knowledge of this dangerous propensity of their pets, they may be strictly liable for the harm done by the animal.
Lastly, the act itself of keeping a snake as a pet may be considered a “dangerous activity” presumed to have great risk of harm. In California, for instance, a person is required by law to exercise extreme care and caution when participating in such activities. If a person engaging in dangerous activity failed to do so, and this failure led to another person’s injury, he or she may be sued for negligence.