It's really great that you are self-aware enough to notice this. Many people go to sleep at night with the television blaring and it's usually because they can't stand the noise (their own thoughts) in their head and so they can't sleep otherwise. This is not healthy.
If you are terrified of silence, you should probably ask yourself why. What would be the worst thing that would happen? Perhaps you might find that you don't like some of the decisions you have made in life. That would be good to know now instead of later in life when the cost of a bad decision will just snowball into a huge avalanche.
I wouldn't recommend that you meditate so that you can be ok with the silence although that's not a bad idea. But it might be a good idea to go out to the beach or the woods or somewhere safe where you can look at everything around you and soak it in and don't bring your ipod. Just listen to the sound of nature and see if you can't hear silence between your ears. Most of the time my "inner voice" is saying lots of stuff and I have been able to sort out the good from the bad and most of it is bad (as in being too self-critical), but the good stuff can save your life or your personal happiness. The good stuff might be something like "this is the fifth time that person has canceled on me and I haven't done anything like that to them; I'm going to find someone else who won't waste my time." Or "man, I really did a good job on that thing the other day. How can I use that in a good way to further build my career/relationship/whatever."
If you can tune into to what's going on between your ears, then you have made a really huge step. Some people can never do this because they are numb. They can't tell you how they are feeling and that's a shame. They should make more trips to the beach or wherever makes them happy and give themselves the opportunity to sort themselves out.
If you can get to a point where there isn't any noise at all and you have no fear of silence and there is a smile on your face, then you have reached a particularly good level of enlightenment. Enjoy it. Anything worthwhile can be yours at that point.