People generally use the expression "make my way home" when they are speaking of going slowly. For example, you may be walking through deep snow and you have to "make your way home". Another example of "making your way home" might be while driving through heavy traffic. Saying "go home" is less descriptive. It just means returning home. Hope this helps

I agree with Naomi's answer. Also, "make my way home" is less aggressive and gives a friendly feel. "go home" sounds very demanding. If someone says "go home" they may be angry at you and want you to leave them alone.