I think your contact was really safe and HSV genital infection is highly unlikely, though not impossible due to the brief oral contact, but still, unlikely.
The lesion you describe does NOT sound herpetic to me due to the pus and because it was a single lesion. The other symptoms are too general to be likely herpes.
Overnight transportation is not absolutely required, but I believe the sample must reach the University within 5 days at the outside. I’ve had not anyone do this from the UAE, no, but if you want to do it, I am happy to work with you.