The bomber is believed to have mailed two packages from a FedEx drop-off center in Austin, the source added.
The former New York City council speaker criticized Cynthia Nixon a day after the "Sex and the City" star announced her candidacy for New York governor.
The shooter — identified as Austin Wyatt Rollins, 17 — was injured and taken to the hospital, where he died, officials said.
Suicide deaths have been increasing in the U.S. and are the third leading cause of death among teenagers.
The Minneapolis police officer who fatally shot Justine Damond is now behind bars and charged with third-degree murder and second-degree manslaughter.