I have a question:

I'm right-handed and I hold a deck of cards in my right hand...Is that normal? A lot of tutorials say to hold it in your left hand so you can use your right hand to do the tricky stuff, but when I do that, it doesn't feel right!

It is more a matter of preference than anything else. Plenty of left handed magicians. Many a right handed person is actually a left handed person who was taught to be right handed, which may be your case. Card tricks work either right or left handed, you just have to move in the opposite direction of the right hander.

Before I started studying magic I used to hold the deck in my right hand as well.
In my first magic book, TRRTCM, it was suggested to hold the deck in your left hand. I thought that is the correct way to do it, I had no clue that it really does not matter. Take Lee Asher as an example;) I started studying card magic holding the deck in my left hand and after a while it just felt right. Don't put yourself through that, I just did not know at the time.
There is nothing wrong in holding the deck in your right hand when performing.

-Matt

Thanks for the advice! You've put my worries to sleep!

The funny thing is I am a right handed person, but for some tricks I am a left handed magician.

That's a new one Ray, hehe! Since I started practicing using my left hand, I stopped feeling comfortable using my right hand.

-Matt

I can see by your picture! ^.^

Yeah, I know what you mean. I'm also right handed, and sometimes catch myself holding the deck in my right hand. Also, I learned to hold my thumb fan or pressure fan in my right hand, but none of the numbers show.

Notice, in matt's pic, the fan is in his left hand, and the numbers ARE showing.

I say just do whatever is comfortable for you if it only affects the trick/sleight in very trivial ways. Sometimes, it is good to learn a trick/sleight both right handed, and left handed, so you don't have to suspiciously shift your body position in order to get the spec at the correct angle.