nejohnson:
I am going to be snorkeling on vacation...I'm going to try to dive down as deep as possible and see how my ears respond.
I suggest you do this in stages. Don't dive past the point where you feel pain. Go down as far as you can comfortably. Try to stay at the barely comfortable level as long as you can, hopefully long enough to try that nose pinch method (valsalva) described by someone else earlier. You will almost certainly have no success at all at first, and you probably won't get very deep. Be patient. Do it again. And again. Eventually, you will find yourself getting deeper, and the valsalva may suddently work, enabling you to go even deeper. Again, be patient. It will take you a while to get the results you are looking for.
Don't be a hero and dive with pain--it just makes things worse.
One thing that will help is improving your breath hold time.
One way to do that is to hyperventilate before you dive. This means breathing in and out very deeply at least three times before you dive. (Don't overdo it to the point that you risk blacking out!) The goal is to get rid of carbon dioxide, the buildup of which is what gives you the frantic urge to breathe. (Lack of oxygen, surprisingly, gives little warning.)
The other way to extend your dive is to dive gently, with minimal body movement. Begin your dive with a simple pike (90 degreee bend at the waist). Don't use your arms, and don't kick until your fins are underwater. Kick gently and casually while you are under water, swimming calmly with your arms folded.
If you eventually find that you can get down to 15-20 feet, then I think you should be able to dive. The first 15 feet are the toughest to deal with in a dive. Once your ears are equalized past that level, you can usually go to almost any depth without too much difficulty.