You certainly can sue for back pay. More information is needed on the raise.
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This is NOT a WC question because you were not injured.
What is the proffered explanation for not receiving monies owed? If need be, it would be far simpler to file a wage claim with the state.
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Sounds like you have a claim under the New York Labor Law for back wages; penalties may apply as well as recovery of attorneys' fees. Look to the written company policy as to raises.