Arbitration is not suing, arbitration is a binding remedy that does not result in further suit.
Certain types of wrongful termination fall outside a Collective Bargaining agreement, because of violation of statutory rights that can't be limited by a CBA, and suit can be brought, and emotional distress is a damage that can be sought in a wrongful termination suit.
I don't see anything described here that falls under a statutory right falling outside a CBA. So it appears likely they are limited to their grievance/arbitration procedure and it is doubtful anything for "pain and suffering" or emotional distress would be recovered that way.
I am a California attorney and cannot give legal advice in your state. My comments are information only, based on federal law and general legal principles. YOUR STATE MAY HAVE ITS OWN LAWS THAT OFFER SIMILAR OR GREATER PROTECTION. If I mention your state’s laws, it only means I did a quick Internet search and found something that looked relevant. You MUST check with an attorney licensed in your state to learn your rights.
If the workplace problem is based on a statute, such as any of the laws prohibiting on-the-job discrimination or protecting whistleblowers then a private attorney may be able to help. If the workplace problem is due to the employer’s dissatisfaction with work or conduct, the remedy is probably limited to going through the union.
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