A.S.
A little late in responding; however, my son, 19months, had the same issue for 9 weeks.
We did all the tests, took all the above medication until I refused the last prescription the doctor wrote.
We did a chest xray to rule out pneumonia, but like the doctor said in the first place, it was nothing, and though it went on for a while and kept us up most nights, it went away on its own.
Not saying you should wait this long, but don't want to medicate everything unless it's totally necessary...then your child's immune system won't develop properly.
Hope allergies are not the issue and it goes away on its own.
Good luck!