Well, it seems that if you were approved for a raise, your acceptance wouldn't have an impact or expiration date. Also, the explanation from HR doesn't make sense, because they can simply give you a raise. So, I think you are being sent mixed signals.
In Texas, you are an "at will" employee without having a written contract or union membership. The wage you receive is strictly open to negotiation between you and the employer. Ot, as stated, the employer can simply give you the raise without any discussion at all. This is the normal course of action.
As far as suing the, no. It would be good money after bad. Unless you have something in writing that promised a raise on a date certain, it is not likely to go anywhere.
If you do have information in writing, you should definitely visit with a local employment lawyer and sit down for a consultation. There is no substitute for that.
I hope this helps.
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