Okay, I'm really scared of dying and it terrifies me just thinking what will happen after you die, eternity and all this stuff! It makes me feel so weird and makes me come to the point of crying and thinking about my parents dying. What is wrong with me? :(

Everyone is afraid of dying... it's the abnormal people that don't... or those close enough to it they've made their peace.

Fact is everyone dies... always been that way... always will be.

You are 13, right? Interesting! I'm thinking back to 13 (53 years ago) and what I thought about death back then. I went through 'something,' not a fear, but a pre-occupation with it. I thought I had invented pantheism, the idea that God is in everything. And that when we die we float around the earth as spirits, not somewhere in a heaven above the clouds. I found that very soothing. But I also thought about death in terms of how angry I was at my mother and how I would die in an accident and she'd be sorry. I had just read Tom Sawyer and wanted to go to my own funeral. Preoccupied with death? No more than any other teen who thinks and reads and has problems.
Advice? You'll get through it. It's part of growing older. Not too long ago, you, your parents, and everyone would live forever. Now you realize they don't.

You should look at various religious concepts and see if any of them are right for you.
On the other side of the coin, some folks look at the fact that their status of not being alive after their death will be the same status they were in - before they were born. The only problem with that theory is whether there is a hell.
If you really want to boggle your mind, consider what it would be like if we all lived forever. Would we get continually older with all the infirmities that come with aging, stay at a perfect health age forever? I haven't been able to envision any options that would work.
To answer your question, there is absolutely nothing wrong with you. I think that wondering about your parents dying is the mind's way of preparing you for that eventuality. And the more you study and think about life and death and how it works and what the various religions say about it etc- the easier it will be for you to come to terms with the facts.
Edit- have to remove bolds frequently as of late, that I didn't put there and which change the meaning of my words.

When I was your age (a thousand years ago), I too, and like joypulv, went through the same kind of phase as you are now. I would babysit my younger sibs when my parents would go out to a party or movie, and if they weren't back when they had told me they would be, I would begin to freak out, thinking they had died in a car crash or had been killed by some evil stranger, when in actuality, they had stopped on the way home for ice cream or maybe the movie had lasted longer than they thought it would.

Yes, you are realizing we are all mortal beings. That's good because you are learning how precious life is and appreciate it with all its blessings. Many people I loved have died, but 99% of the time they were old and sick, so death was a good thing that released them from pain and earthly problems. When young people die, too often it's because they engaged in some kind of risky behavior with fast driving or taking street drugs or because they don't talk with helpful adults about their problems with bullying or depression and then take their own lives.

So my message to you is take good care of yourself mentally and physically. Get help when you aren't managing well on your own. If you're worried about the afterlife, visit a few churches to find out if any of their messages comfort you. I figure the world did just fine before I got here, so I'm sure it will do just fine once I'm gone. And I do look forward to an afterlife that's much nicer than this one.