How can I have my own design printed on fabric?

I bought these pink and brown damask pillows at a crafts store and I want to decorate my niece’s room with this pattern. The problem is that I cannot find the exact pattern or if I do find something “similar” it is way off.
I want to know if I can just take the pillow somewhere and have someone make the same design on some fabric I have. I need to make the curtains and bed skirt and the other nursery items.