Dear Diver to Be
Welcome to the scubaboard. You have come to the right place for information, and I am sure that many of the knowledgable people here will have good and workable solutions for your problem.
I just started diving and therefore cannot give you any advice, but I did want to note that I had the same problem. I did notice, however, that this only happens when I get uptight or excited and "unrelaxed". I also had this feeling of not being able to get a full breath from the regulator until I learned to take it easy and not inhale like I was never going to breathe again. Remember that the air you are breathing is compressed under water and even if it feels like you are not filling your lungs, you are still getting plenty.
My suspicion is that this is a beginner's problem and will go away when you become more familiar with the whole equipment/feeling/learning process. After a few dives, the problem went away for me.
The good folks here will have some better advice for you, though, so keep checking in!
gozumutti