In New York, non-compete agreements are generally disfavored, however a non-compete agreement is still enforceable. The agreement cannot be too broad and cannot unreasonably restrict a person's right to earn a living.
You would need an attorney to review the agreement you signed and the job description for the new company to determine if it might be enforceable. Another question you need to ask yourself is whether even if the non-compete is found to be invalid in your case, if it is worth the cost of potential litigation.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
If your noncompetition agreement is enforceable requires more facts and review of the agreement, in addition to being licensed in the state at issue. As a general matter, many states allow noncompetition agreements provided they protect a significant business interest and do not unreasonably restrict the ability to earn a living. This test normally requires that the agreement is reasonable in: (1) the scope of activities sought to be limited; (2) the contract's duration or time restriction; and (3) the geographic restriction.
You should speak with an attorney regarding your issue and provide them all facts and the agreement. Contact people you know and trust for referrals. If you have no referrals, contact your local bar association for their referral program. Good luck.
DISCLAIMER—This answer is for informational purposes only and discusses general legal principles, trends, and considerations and is not intended as specific legal advice regarding your question. This answer does not establish an attorney client relationship. For legal advice, you should retain legal counsel regarding your specific circumstances.