I dont feel well中,feel是系动词,well是表语,系动词和表语组成合成谓语.这里well是形容词,它和feel不是修饰关系.副词可以修饰实义动词,它们之间才是修饰关系.例如.He looked angrily at the man.这里副词angrily修饰实义动词looked.

I don't feel well.
I am not feeling well