Generally speaking, doctors are discreet. If they aren't, they can lose their licence. Ontario College of Physicians and Surgeons has a list of doctors taking new patients.
There is a walk in clinic at Bay and College, south west corner. If you go early, you will have less wait time.
Hassle Free Clinic specializes in STIs. They are at Gerrard and Church. Check their web page for their hours. Its different for men and women.