Checking for uniqueness within a string
This solution is inefficient:


There is no point counting the characters in the entire string: once you found a duplicate, you can stop counting, because you know the result is false


This also implies that the map of counts is wasted space

Iterating over the alphabet to check character counts is inefficient: it would be better to iterate over the map values


Instead of a map, it would be more efficient to use a set.

Instead of a set, you could also consider a boolean array of the size of the alphabet, values initialized to false,
and use that to track characters seen so far.
The disadvantage of this approach over a set is that it might use more space.

You are also violating some good practices:


using namespace std is considered bad practice
readString is poorly named: it doesn't "read a string", it initializes a map of character counts to all zero values
No need to pass stringLength together with testString. You can derive that value from testString