^Come on, that's not true. Any warm body is required by law in both the United States in Canada to receive life-saving care like the delivery of a baby or the treatment of an infection, even if it's self-inflicted. OP, don't ever have the attitude that medical treatment is totally unavailable to you, because it's not. Truthfully, they'll treat you for a lot of other shit short of actual life-saving treatment in most cases, but not all.
My advice would be to find a way to get some medical advice regarding your situation if it doesn't improve or gets worse. While it's true that oral antibiotics would be probably be the first-line treatment for this sort of thing, not all antibiotics are ideally suited for every instance of infection. Certain antibiotics exert a stronger influence on certain specific bacteria, which could potentially involve your physician prescribing a different course of antibiotics to treat your injection complication.
Also, alcohol is great if you don't have access to soap and running water i.e. out on the street, but the ideal situation would be that, to use soap and warm water to clean the site. Not nitpicking, that's just HR stuff. Anything that can help minimize complications is great.