What do you need it for?
I don't understand why you first reace it and then open it in Photoshop.
When you trace this, what Illustrator does is create shapes. Lotos of shapes, because it can't make gradients. And also it puts them exactly side by side. You can try the overlapping option in the Image trace panel.
You can only expand the trace afterwards, select all the white shapes (possibly only one) and delete them.
Are they "real" lines: when you zoom-in do they get bigger?
They may just be an artifact of imaging such a complex drawing.
Save out to pdf, can you see them in the pdf file?