Sheets - no.
Towels - maybe, IF it were still wet, and only herpes. Chances are really slim, and this is more of a theoretical risk than anything. This isn't anything I'd worry about.
Sexually transmitted infections require some kind of sexual contact to transmit, and casual contact/living with someone doesn't transmit them. You won't get any STD from a toilet seat, sharing a shower, etc.
There are some fungal infections (yeast, athlete's foot, etc) that could be transmitted through living environments, but those have nothing to do with sex. It's important to know that people with STDs are not walking, talking biohazards. Things like colds, flus, strep, etc., are far more infectious than STDs.