can I use the dc motor shield to control these 4 motors with such high current?
The way this question is phrased, one would think that there was only one dc motor shield made. That not being the case, you need to be more specific in defining which dc motor shield you are talking about.
Typically, though, the kind of current you are talking about will fry most motor controller boards. There are controllers that will handle that current, but they tend to be expensive. If you paid less than about $200 US for yours, and it doesn't have massive heat sinks on it, it most likely won't handle the current.
if not, what are the alternatives I have ?
Learn to use capital letters as required, and spend some time with your favorite search engine.