That's not really the purpose or scope of PRIA, but your training records do become available. Disciplinary action may be, but most employers prefer to disclose the minimum (often summed up as yes we would hire him again, or no, we would not) do to the potential liability of saying too much.
You didn't indicate the type of operation for which you're flying, but it sounds like you have minimal experience in an airline (or union) environment.
Don't argue with scheduling. Dont' ask them for contract references. You ask the union and your steward for that. If this is an ongoing problem, then grieve it, discuss it, see if it can be addressed via your union. Unless you're a steward (and it sounds like you're not), this is not the windmill at which you should tilt.
Do not tell scheduling that you'll be filing a grievance. Scheduling does not work for and is not associated with the union. They have nothing to do with your grievance. It sounds like you're trying to threaten them, push them, throw your weight around. Don't do that.
You made a point of saying that you didn't get loud or profane. That should go without saying; it shouldn't be a remote consideration, but your having said so makes it sound like you were doing them a favor or acting out of character. You should never be getting loud or profane with the schedulers. Thank them for their time, and contact your steward. You have representation, if you have a contract: use it.
Grievances will either be approved, or taken to settlement (or arbitration, if warranted). That's for your representatives to handle.
If you've garnered the attention of the chief pilot, this should be a red flag for you to step back a bit. If your contract has relief for the trip from which you were pulled (ie, if you should get the value of the trip time, rig, etc), then grieve that if actionable, or move on if it isn't.