It really depends on what exercise you are currently performing. If you are doing compound exercise such as the Bench Press or Squats for example. You will not necessary feel a pump in any particular muscle as several muscles are working together when lowering and lifting the weight.
When doing isolation exercises which are mainly done with a dumbbell such as the Dumbbell Curls. You are more likely to feel a pump in your muscle since this type of exercise is primarily focusing on exercising just one muscle.
Also if you are not feeling it in your muscle when working out this could simply be because you are not lifting a heavier enough weight. Having said this not feeling anything in a muscle you are focusing on with your training is not necessarily a bad thing.
Going into a training session thinking it's a good thing that you should workout until your muscles are sore. Is the sure fire way to inflict injury and tears on you muscles which is a very unpleasant thing to happen.
So never work yourself into the ground each time you lift weights. Sure when you are new to weight training or trying a new exercise. Then your muscles will usually feel sore afterwards because they are not used to the new stress you are placing on them.
But if this soreness does continue for a long period of time then I would take it as an indication that your body is tired or that an injury is developing in the muscle. If this is so I would either rest for a week or lift a lighter weight until the muscles have recovered.
Read more here about the science behind gaining muscle quickly
Read more here about the science behind gaining muscle quickly
