Such claims are extremely difficult.
Historically, one could not even sue the government (which runs the schools) until the late 1970's, under the theory of sovereign immunity, or, as they said in the old days "the king could do no wrong." So, even now some 30+ years after the erosion of sovereign immunity, the courts and legislatures have kept certain barriers to suing governmental entities.
If the trainer and others were involved in a discretionery function, an area where they had some choice, they are immune. If the trainer, was giving you advice, a workout program, or other assistance which could be viewed as reasonable in the circumstances, then there was no negligence.
You might look around for an attorney in your area who has had some success in this type of suit and get a consultation in which you can give them your "long version" so that you can get a more detailed answer.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.
In addition to the answer provided, I would like to add the following:
1) Whenever you try to sue a public entity/municipality in New York State - such as a school district - you usually have to file a Notice of Intent to File a Claim/Notice of Claim within 30 days of the alleged negligence. You really should speak with a Personal Injury attorney in your region to help with filing this document. It must be done in writing and must comply with the provision of the applicable state law.
2) In many sports injury cases a person has assumed the risk (or perhaps even your parent(s) assumed the risk) of your getting injured in a sports-related accident. You should check with an attorney to see if the doctrine of "Assumption of Risk" might apply in your particular case.
Best of luck.
THIS RESPONSE DOES NOT IMPLY OR CREATE AN ATTORNEY-CLIENT RELATIONSHIP. NO ATTORNEY-CLIENT RELATIONSHIP IS IMPLIED OR CREATED BY RESPONDING OR FAILING TO RESPOND TO THIS RESPONSE. THIS RESPONSE DOES NOT PROVIDE LEGAL ADVICE. FOR LEGAL ADVICE, YOU SHOULD CONSULT AN ATTORNEY.
Sign up to receive a 3-part series of useful information and advice about personal injury law.