To my knowledge, most of the STDs are not zoonotic diseases. Meaning they won't cross the species barrier. i.e. you cannot give them to animals nor get them from animals. HIV, HPV, syphilis, chlamydia, gonorrhea, hepatitis, etc al. are all human-only. Off the top of my head only brucellosis and trichomoniasis were ever concerns for us zoos as being possible to sexually transmit, but they can also be passed nonsexually between humans and animals, so there's an out-of-band plausible explanation if you ever caught them -- and they're are rare enough you stand almost zero chance of that anyway, especially from a domestic companion animal (the latter, trich, really only prevalent among infected bulls in a cattle herd). So as dogluver101 said, unless the animal is merely acting as carrier not host, eg. going right after an infected human in a share scenario, you aren't likely to ever catch anything that isn't 100% explainable and treatable with ordinary antibiotics (explainable as simple exposure from living in close quarters, handling / cleaning up bodily waste, etc.). Deagle will eventually see this and chime in if I'm wrong anywhere.
And for those of you without health insurance, well you didn't hear it from me, but rural feed stores and Tractor Supply sell injectible antibiotics (tetracycline, bactricillin etc) and several gauges of needles. All OTC, no RX needed, no questions asked. They assume you're dosing livestock. Now of course dosing ourselves is very off-label and highly discouraged as these are "for animal / veterinary use only" but I'm not gonna say us poor farmers haven't tried 'em when we need to clear up something, and its worked so far... I haven't grown a third head or sired a minotaur yet. Not even grown me a tail or a knot or a corkscrew, to my disappointment...