Toilet and shower will not drain
You have a blockage further down in the pipe that services your shower, toilet and sink. That's creating a sea of liquid that comes out at the lowest available point (i.e. your shower). Drain cleaner will be worse than useless; while a pool of poop may be nasty, a pool of caustic poop would be even worse. A 5' or so drain snake won't do it; you probably need something much longer, and a way to get it into the pipe (past the traps on whichever device you enter through). And, until you've cleared it, stop adding liquid to the situation.