I'm going shop和I am go shopping, 这两句话都是有语法错误的.
go后面加动词的ING形式表示去做某件事.比如楼上说的go fishing,去钓鱼；go swimming, 去游泳.
be动词后面接动词的ING形式,比如I'm running,而不是 I'm run.
be going to意思是将要做什么,但是I'm going to go shopping不符合英语的常用习惯,也很拗口,所以如果说我要去购物,应该是I will go shopping,或者I am going to the shop.