When backing up, I've got to really press the brake pedal very hard to stop the car. Then when going forward, it's still hard for 2 or 3 presses, then goes back to normal.

 

Sticky caliper/wheel cylinder?

 

Update: I've noticed that now it isn't just when backing up. It's any time I press the brake now. If I ease into it veeerrryyy slowly it's fine. If I press it normally while coming to a stop at a red light it's really hard and hisses at me.

 

You have a bad booster. Check the vacuum line and the check valve going to the intake manifold for leaks.

 

I think you're right. I just followed some steps from another site:

while the engine is off, press the brake pedal several times, hold 15 seconds. It should not move... pass

press brake pedal and turn engine on. If it sinks, booster works. If it doesn't move, booster is faulty... fail... pedal did not move.

while engine is on, press the brake pedal, then turn the engine off. If it doesn't move in 30 seconds, it's fine, if it rises, booster faulty... fail... pedal pressed up against my foot.

check valve test: disconnect line from booster, start engine and let it idle. hose should have a vacuum... pass

Looks like I'll be investing in a brake booster very soon.

Thank you for helping.