Even though you say she won't go to the doctor, that's what she needs to do. Go to a hospital out of town and use a fake name if you have to.
Even though there is a *chance* that it is not an abscess, it is not worth waiting. Not unless losing a foot is worth it to her. Infections like this are very serious, despite hoping it isn't. It is not something to play around with.
Trying to lance and drain an abscess would be extremely dangerous. Even if you somehow managed successfully remove it (which would be extremely difficult and painful without anesthetics), she would most likely need stitches or at least medical service provided from medical professionals afterwords.
The foot is also a very bad place to get an abscess. It's already not advisable to IV there, because of low blood flow and the possibility of blood clots, but missing a shot there is much more likely to form an abscess because of the aforementioned reasons.
An abscess does not "run it's course" or "heal," in the traditional sense. Although there is a small possibility that it may go away, there will be lasting damage from infection. Usually "running it's course" means forming, infecting, and eventually needing removal of the affected area via draining, some sort of surgery, or amputation.
If it is actually an abscess, which it sounds like is starting, she is walking a very dangerous path by not seeking medical attention immediately. Hospitals in the U.S. are required by law to give emergency medical attention when needed, regardless of insurance or even legal citizenship. She doesn't have to tell them what happened, she could say while fishing a hook caught her foot, that is not uncommon. Ever wonder why gangrene is often associated with fisherman?
Depending on how far along the abscess is, it may have epithelialized with skin, meaning that antibiotics will not reach and resolve it. Even if it hasn't, a well formed abscess usually has to be drained due to antibiotics not penetrating to the center of the infected area.
The clear fluid coming out doesn't mean that it's not infected. It MIGHT mean that, but it could also mean the infection is too deep to come out right now. The clear fluid is most likely some sort of plasma or much more unlikely, some of the missed injection.
It's possible she blew a vein. Did she get a rush/high from the injection? Is it bruised? Did the pain onset very quickly, almost immediately? Even if she answered yes to all of these questions, it doesn't mean it's okay not to seek medical attention. Do so promptly.
I hate to be the bearer of bad news, but that is her only safe option. There is no reliable alternative to surgical incision and drainage of an abscess. Heat alone may help small superficial abscess to resolve, but the degree of epithelialization can vary dependent on many factors, and will most likely cause the abscess to reappear. Doing anything else is nearly guaranteed to make it worse and delay the inevitable (medical attention).
I hope this was informative enough to convince you to go seek medical attention from an ER. If it's not, I can post some pictures of abscess and maybe that will convince you.
-A120
EDIT:
Figured I would post them anyway. Not going to hospital is a terrible idea. Nothing is worth losing a foot over.