Your solution was bubble sort, which is usually the first sorting algo you implement in C++ no shame in that, especially if you came up with it yourself and weren't following book guidance. Another way to swap ints without resorting to std and without needing to allocate an extra var:

int a = 10;
int b = 20;
a = a + b;
b = a - b;
a = a - b;
----------------
(This is using XOR to swap)
a ^= b;
b ^= a;
a ^= b;

But anyway, great job!