No, it really shouldn't hurt that bad. It might feel awkward, but if you are feeling pain, it is probably either because you are too tense, or have your wrist or arm at the wrong angle. If you continue to hold it the wrong way it can lead to carpal tunnel syndrome.
I would try and find a private teacher, and maybe take a couple lessons just to make sure that you are holding the instrument correctly. The hardest thing about holding it, is that there are so many little things that you might be doinh, and they can cause your entire hand to cramp up. I had a student who just needed to bring her arm in a little bit, and it fixed her entire hand position, and it didn't hurt anymore for her to play.
Good luck!