Kim, be aware that what you need to do is create as much space as possible for you lungs to expand. In good singing technique, breath support means many things happening at once that you learn to do until it is automatic, and you don't have to "think" technique. Being able to relax during the breathing in and singing out is part of it, too. So, all these things take consistent practice while you are singing. We breathe from our lungs, not our diaphragm, so that old phrase of "breathing from your diaphragm" confuses alot of people. Just think of it this way. The floor of your abdomen holds up your internal organs. When you learn to hold those muscles down, you create more space for you lungs to fill with air. If you are really breathing deeply enough, your bottom ribs will exapand and your diaphragm will go down, because you are pulling your "guts" out of the way. Again, your shoulders should not move up. Your air should be a smooth flow in and out, and that takes practice.
Kim, my voice teacher called while I was typing this, and I read your comments to her. She said that you may be gasping air in (grabbing it) with your throat muscles, and your voice will tend to crack because the air is not an even unobstructed flow. If you are trying to bring the air in too hard and fast, you will gasp and create this problem. It will solve the problem if you breathe through your nose instead of your mouth. It could be something else causing that feeling you describe, but this is the most common reason. She says it sounds like you are grasping at air with your throat muscles. You need to develop more smooth breathing. Breathe through your nose, and you will have no danger of getting the neck muscles involved.
Relax!!! Breathing through your nose also helps filter out dust and other stuff in the air. Using those muscles to pull your guts down when you breath in will provide enough air for volume and sustaining a long phrase.
Alice