Right to a Speedy Trial

I got a question here. (I'm in NY)

I had an argument with my wife on May 30th and I was arrested that day. I was charged with 3 misdemeanor and 1 violation.

According to the NY law:
Defendants are entitled to a speedy trial, which under New York law means ninety days for an A misdemeanor and six months for a felony.

My first court appear was on Jun 16, and my lawyer aggressively requested for trial.

The case was adjourned 4 times and my last court appear was on Oct 3, which is way over 90 days and it still got adjourned to 10/27 and my lawyer didn't say anything.

Can I sue the court or prosecutor???