I always recommend doing a dry draw before lighting your tobacco for this very reason. You should be able to draw from your pipe as easily as drinking through a straw; if you have to try to draw, then chances are there is an obstruction somewhere. Typically, this is the result of packing too tightly.
I believe everyone has to find their own method for packing efficiently, and that that method has to also be flexible enough to accommodate different chamber shapes/sizes and tobaccos (some expand a great deal when lit, and others hardly expand at all). It just takes practice and time, as well as getting familiar with your new pipe.
One thing I sometimes do if my draw is constricted after I'm already partially through a smoke is to run a pipe cleaner all the way to the draft hole, as gently as I can. Usually, a bad draw is the result of tobacco being packed too heavily at the bottom, and pushing some of it out of the way can help. Running a pipe cleaner every now and then also just helps with providing a dry smoke generally.
My experience with Neerups is that they are typically large pipes with fairly open draws. Based on what you're saying, I think your packing is off. It may be too tight, but a pack that is too light can result in the same problem, i.e. a light pack makes it more likely an errant piece of tobacco will be drawn into the draft hole and/or inside the stem.