Hi
There is a STD doctor at Hamad Hospital who will see you discreetly.
I knew someone who went there and you book in at reception and then are directed to one of the upper floors. You don't even need an appointment.
All the employees are professional and don't take the p*ss (to your face).
It isn't illegal and you won't be in trouble with the law.
Good luck and next time wear a Johnny.