A question about height/weight

I am 14 (soon to be 15) years old girl, Asian. I am 155-157 cm tall, and after dieting I became 38 kg. I don't want to grow in height anymore, but I want to get heavier. I haven't really grown in height since I was thirteen. Is there any way for me to gain some weight but NOT gain any height?

You could always try to gain some muscle,which will add useful weight to your body.
You could lift some weights, although start with smaller ones to prevent straining any muscles. There are also weights you can attach to your body that help you build muscle during your normal daily routine,such as leg weights. So when you're simply at home, you could build muscle by walking around!
Walking in general builds muscle on your lower leg, and so does cycling.
So I would truly recommend giving these excercises a try.
Good luck! It's good to finally hear somone wanting to gain weight, instead of trying to lose it.