c++ Checking if a string is an isogram
Avoid using namespace std.

Keep your lines shorter.  Having to constantly scroll back and forth to read lines is unpleasant.  Most of your comments should be on one (or more) lines right before the statement being commented on.  Also, avoid obvious things in comments (like "resets i to use in the next loop.").

Declare variables as close as possible to their first use.

Since isogram_check is a bool, you can test it with !isogram_check instead of isogram_check == false.

With a slight change in algorithm (searching characters before the ith one), your two while loops can be combined into one. Although there are other ways to do this that could be better (for some definition of "better"), your implementation is a quick first pass that works well for short strings (but less well as the strings get longer).