Not at all, Jenny... unless you want them to be. I can only speak for saxes, but I guess the same applies to clarinets as well though.
It will largely depend on the style of music you're interested in. If you're going for a mellow style, then the clarinet has a wonderfully warm lower register. Even at the top, high notes needn't be shrill in the right hands. You'll develop your own style eventually, and it certainly doesn't need to be painful to the ears.
This is where a good teacher comes in. One of the biggest concerns is the right mouthpiece/reed setup for you. Classical players largely go for a small tip opening (mouthpiece) and a very hard reed. This gives a tight, controlled sound and great accuracy needed for classical music.
Those of us on the Jazz/Rock side go for a large tip opening with medium to hard reeds. It's harder to control, but lends itself to very expressive, bigger sounds.
Welcome to the world of mouthpieces and reeds, Jenny. You'll wish you never asked ;o)