As a lawyer, I dont see what you'd be suing for, or whom. Rude service is not a reason for a lawsuit. It doesn't look like you've gotten your bag back yet, so there's some basis there, but there's also the rules of carriage that limit the airline's liability there.

I'd suggest complaining to AA again, trying to get them to bump up their voucher offer beyond $175 and hope for the best.

Suing will cost you more than you could ever hope to recover, and because so little money is at stake here, I doubt anyone would take this on a contingent basis.