Let pain be a guide. Some post workout soreness is normal, especially in untrained individuals, but, acute pain means STOP.
Working out harder is generally not conducive to better results because weight training is a highly intense activity and you need substantial recovery.
Generally, a program of periodization will be a way to success.
You need calories, time to recover, sleep, and stimulation, but, not over training.
Like a ship, steady as she goes.
Plan for success, stay injury free, and EAT, which, is, by far the single biggest factor that will affect your gains.
You may well find a that light "pump" session with high reps (ride a bike, reps of 25, etc.) will serve to hasten your recovery and lower soreness.
Stick with moderate reps (6 to 15, or even 8 to 12), and get pumped up, then, GO HOME; EAT; SLEEP.
While you can build a bit more strength by lower reps, injury is more likely, and you won't see the muscular hypertrophy that moderate reps will bring.
If sarcoplasmic hypertrophy is your goal, you'll want to keep the reps up; keep the calories up; not overtrain; be consistent, or even take a few days off every so often to help with recovery.
You make GAINS when you're NOT in the gym.