Glad you found the cures. A few things that'll make the disease loop much less painful:
You don't have to apply cures by hand.As long as you keep cure potions in your brothel's item stash, the game auto-treats any infected girl at the end of each turn (this is on by default, it's the "automatically use items" setting). So the move is to buy a few cures whenever the shop has them and just sit on the stockpile. The Elixir of Ultimate Regeneration is the best one to hoard, since it cures all the STDs (and clears up scars and other afflictions too), rather than the single-disease cures.
Hire a Matron. A Matron pulls diseased girls off duty and warns you in the turn summary, so you catch infections instead of finding out the hard way. Without one, a sick girl will keep working (and keep spreading it).
There was a bug where girls could catch STDs out of nowhere, even from a clean player with no interactions. That's fixed in the upcoming 1.15 release.
Yep, the up arrow on each girl's profile bumps her housing level, which keeps her happier and better rested. The mechanism will be redone in the future