If you have not already, report the accident to the police. The responding law enforcement officer should be able to determine if you were fully at fault or partially. Some states allow for comparative negligence which when applied in accident cases it is to determine responsibility and damages based on negligence of all parties directly involved in the accident. With this it might be decided that both you and the neighbor are both responsible in different degrees.
For instance in Ohio they have comparative negligence laws that state parties share the cost of damages from an accident in proportion to the share of negligence. A motorist determined to be 50% or less at fault may recover their damages minus the percent cause by their own negligence. If more than 50% there would be no recovery for losses from the other party.
Other states, such as North Carolina, apply contributory negligence which means that if you are even slightly at fault in a collision you are not entitled to any recovery against the other driver. If this is the case, and your state has this law, and your neighbor is found at least partially at fault you each would pay for your own damages.