Exactly, our current cat was scratchy when she was a kitten, in kittens claws are a novelty, just like babies who have teeth, but we don't go pulling those out! Your cat will calm down, our cat started clawing the wall in the kitchen when she was hungry, so we put a wall mounted scratch post there and now she claws that. Obviously occasionally she will claw something she isn't supposed to, but when you decide to have an animal that is designed to claw, you shouldn't be surprised when she does what nature intended! Don't make a massive fuss about her being in certain rooms either, we did that with our cat, she scratched our sofa so my mum banned her from the front room, but then when she managed to get in the front room it was a novelty for her and everyone went mad, which excited her and made her scratch more.
Play with her more as well, then she will be distracted by toys and she can get some of her clawing and chewing frustration out on those.
Spaying tends to be done on weight, our cat was six months when she was done, but she is a very big cat.