It is possible that you might have a claim for harassment and it certainly would be possible to counterclaim against your neighbor if he were to sue you.
The difficulty of this situation seems to be, however, that if you receive a citation or arrest for disturbing the peace, your neighbor is not actually suing you. In such a scenario, you are really being prosecuted by the city in which you live. Therefore, you would not be able to counterclaim your neighbor and would have to file a separate lawsuit against him.
If you are working with limited funds it might be worth speaking to an attorney in your local area and figuring out what it would cost to have that attorney write a letter on your behalf informing your neighbor of your opinion and the fact that you are contemplating legal action. In some cases, that might be enough to discourage your neighbor from making any more unnecessary calls to police and would save you the cost of actually going to court.
That being said, every case and situation is different so it is impossible to make a definite assessment based on the limited facts before us. Your best option is almost certainly to speak with a local attorney in your area who can advise you after making an informed assessment of the situation.
This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.