Acne is not an STD, and STD's do not cause back acne. Acne is specifically a term related to a specific species of skin bacteria called, "Cutibacterium Propionibacterium acnes," which is also called for short, "p. acnes" or just plain, "acne." It is part of your natural skin flora, and is not spread sexually. Some people are more prone to overgrowth than other people, due to diet, hygiene, various environmental exposures, including wearing tight or unbreathable clothing, or working out, having certain underlying conditions, such as hormone imbalances, or auto-immune problems, or just genes.
However, if you have an oily back, or work out or sweat a lot, and not wash your back regularly, yes, or just prone to acne in general, then that can cause acne pustules to form, which would be from p. acnes bacterial overgrowth and having sebum clogged pores with dead skin and sweat and oils in them causing inflammation. I mean, although not washing your back may not be the direct "cause" of "your" back acne issues, it certainly could be.
Get a bar of sulfur soap (like Grisi Sulfur Soap for Acne), or salicylic acid body wash (like Neutrogena Body Clear), or some benzoyl peroxide body wash (like PanOxyl), or you can also add tea tree oil to body wash you have, or get a product with tea tree oil. All these products you can get at most drug stores, and if it's hard to reach, then get a back scrubber with a handle, and wash your back. If one of the above doesn't work, try another one, as those three ingredients are the staple acne fighters. People sometimes respond really well to one over another. Although benzoyl peroxide and salicylic acid are generally considered the best two acne fighting ingredients, some people don't like benzoyl peroxide because it bleaches towels and clothes but it shouldn't do that if you wash it off completely. Just make sure you leave it on for 2 minutes and then wash it off completely. And some people think salicylic acid stings. So if you don't like either of those, then sulfur might be your best option, and although it sort of has a funny smell, the bar soaps aren't that bad, and its not noticeable when you wash it off and dry off, and it is one of the oldest and cheapest treatments and is also really effective and often ignored, but it is really good. If none of those work, maybe the issues are yeast or fungal caused, which if so, then tea tree oil containing products, are especially good if your issues might have a fungal or yeast cause component, and yeast can amplify acne problems also.
So see if regularly washing your back with any of those ingredient containing products help, and if not, consider other culprits. Like, make sure you wear clean shirts every day, and wear breathable fabrics, i.e., cotton, etc., and avoid shirts made from synthetic fibers, i.e., polyester and nylon, etc., and also make sure to wash your bed sheets regularly, and drink lots of water.
If none of that helps, make an appointment to see your doctor.