This is actually a pretty good thread! A lot of people out there have blemishes on their backgrounds. Speaking from experience, (I've never had a prostitution case, by the way) a criminal background is something you have to deal with. It sucks to find jobs, and it also sucks to find a place to live!
I've had to change my major in school due to some bullshit. At the moment, I'm doing my basics to secure an education under my belt and I aspire someday to become a criminal defense attorney. If that doesn't work, I'll start my own business.
Also, I'm not sure what the accuracy of this is, but here is a list of employers that supposedly hire felons...maybe they will look over someone who have a prostitution conviction. FYI, If you hire a felon, you get a tax credit!
But in the end, networking and meeting your prospective employers in person sure does beat going online and filling out applications for no response.
Good luck.