There are various ways to write sentence with "nandemo" and "nantomo".
I'll try to answer the difference between "nandemo nai / なんでもない" and "nantomo nai / なんともない"
"nandemo nai / なんでもない"
Person A : You seem a bit down today. Are you OK? What happened?
Person B : Nothing. / Don't care.
This is sort of mental question, and Person B doesn't want to talk about oneself to Person A.
"nantomo nai / なんともない"
Person A : You've been coughing all day. Are you OK?
Person B : No problem. / Don't worry.
This is sort of physical question, and Person B doesn't want to make Person A worry about Person B.
Hope this will help :)