Without looking at your brake system, and never experiencing this myself, I'm going to throw out a whole bunch of things to check -- BUT read the link at the bottom of this post for the best solution, directly from the Toyota Celica Shop Manual.
PROBABLY NOT RELATED: Have you checked your brake fluid? Does it look fresh? Is it giving enough pressure? When was the last time you had it changed... 100k miles ago?
RANDOM: It may be related to weather. Are your pads getting frozen (by water/ice) to the shoe?
POSSIBLE #1: Are your brake pads in the rear still good - or are they thin/warn? Had you been driving on them while they were thin/warn? Have you had your rotors turned
after replacing them?
POSSIBLE #2: Are your brake pad tension or return springs faulty? Did you recently have your brake pads changed -- are they factory OEM pads or just the basic "discount brand" pads? Did they replace the return springs with a new set (usually included in the box with new OEM brake pads) or were the old ones reused?
SUGGESTED: You mainly mentioned about your parking brakes; Here is some information on troubleshooting the brake system...https://www.celicahobby.com/photos/celica/tech/ShopMan2/BR/