I am in the United States. Where I live we have what are called "family planning" clinics which deal with contraception, pregnancy, STDs, patient education and etc. I am imagining this is what you mean by "sexual health clinic", but please correct me if I am wrong.
I am a public health nurse in a family planning clinic of a state health department. I absolutely love it. It can be very busy at times, but I work one on one with patients of varying ages, providing education, counseling, medication and birth control depending on the situation. It is very satisfying work helping people navigate such important life decisions. Giving people the tools, resources and education to make their own decisions and to understand their sexual and reproductive health is, for me, an amazing thing to be fortunate enough to get to do each day.
I cannot speak to the education necessary in Canada. Here, besides the obvious education/licensure requirements, having some experience helps to get your foot in the door. Some of my fellow nurses have degrees in public health or health education beside their nursing degree. Most of the time, it's not that it's necessary to have these other degrees (and they might not have even had them when they first started), but my experience has been that in this specialty there is great encouragement (and even financial help) to learn and keep building on your education.