If I have a mild cold and someone's booked in advance or someone wants to see me and can't wait, I make the situation clear and give them the option to go ahead if they want to. I don't get cold sores, but if I did I'd operate a similar policy and tell them in advance exactly what I would and wouldn't do, then take the booking if they still wanted it. I think it would be very bad customer service to allow clients to find out when they turn up, and if your agency's willing to do that it's not going to do their reputation any good. You already know they suck though.
The strip club I used to work at was like that. We were fined ?50-100 if we missed a shift for any reason (if you could barely move you were allowed to go home after you'd spent a couple of hours at the club, done some sets on stage and tried to sell some lapdances). We were ill all the time thanks to the skimpy outfits, terrible temperature control, getting nose-to-nose with dozens of people a night, and of course spending our working time around other girls who couldn't afford to call in sick.