Oh dang, what a nightmare. These guys get themselves into spots! So, when exactly did this happen? What did the vet prescribe? I wouldn't worry too much about the expiration date, once they mix the drug up it is usually set to expire shortly thereafter and is no indication of the strength. And if it's an injectable, they are good for a few months after the expiration (in NO WAY am I saying it's okay to give expired meds, but if it's an antibiotic and it expires during the course of treatment in all likelihood the drug will be fine).
A vet would be the natural first choice, but it seems as if you are in a pickle. One of my GCC had a green thread wrapped around her ankle and 2 toes. I have no idea how long it was like that but I freaked out. The thread had cut in deep around the ankle and one of the wrapped toes was HUGE. I found this after 8 pm at night. Hubby and I performed a little mini surgery and removed the string and treated the cuts as Laurasea outline above with betadine. The big toe was actually even bigger the next morning and I was pretty sure she was going to lose it. Thank goodness the toe pulled through but it still remains slightly large and darker than the others 6 months later.
If I knew how long ago the incident took place, that would provide a pretty good indication as to the reason for swelling. If the injury is still acute, the swelling just may be part of the natural course for healing. If it is 3 or more days and the swelling had gone down but now suddenly reappeared that points to a probable infection. And of course there is the possibility of necrosis/gangrene. If you have been giving the antibiotics for over 24 hours and things are taking a definite turn for the worse, it could be possible that the antibiotic prescribed to you isn't effective against whatever bacteria is involved. I would never normally even think about it, but if it likely an infection that has a good chance of being fatal, perhaps you need to start brainstorming about getting the "right" antibiotics into him. Perhaps asking the original non-bird vet to provide another drug? Or a phone or online consultation with an avian vet who can prescribe?
For now, there are steps you can take to help the bird whatever the cause. First, make sure his living quarters are as sterile as possible. Make sure the bird is kept warm, warmer than the ambient household temperature. You can use a heating pad or other "safe" heating element. No heat lights or fan heaters, ever. Aim for a temperature of 85 degrees or so. Keep a close eye on how the bird responds. Puffy birds are cold birds and panting and/or wings held out are hot birds. Make sure he has a place to rest that doesn't involve his foot having to grip something. If it were me (I am NO expert and would double check this one), I would consider supplementing his water with pedialyte. Minimize all "avoidable" stressors. Remember, sick birds hide their illnesses way too well. They are a prey animal and if they "looked sick" in the wild, they would be the first one picked off by a predator. And if it is too hard to soak the foot as Lauraesa described, I would be using a similar solution and drenching that entire foot/leg every 6 hours. And try to make sure he eats, even if you spoil him for now with junk. His body needs calories to heal.
I can't think of anything else and I'm sure I'm missing tons. Hopefully you'll get some additional advice from others who know more.