One hundred and fifty years ago diseases like pneumonia, typhus, cholera, anthrax, and even infected wounds where usually a death sentence. With the advent of penicillin and other modern antibiotics most of these diseases and conditions became curable. If the current social and economic order breaks down we could see a resurgence of deaths from diseases and injuries that are easily and commonly treated with antibiotics. As stated earlier, doctors will be in short supply; and medicines, including antibiotics, will disappear from pharmacy shelves within days if not hours. So it might not be a bad idea to include some antibiotics in your medical supplies.
Some antibiotic ointments are available without a prescription. Neosporin and triple antibiotic ointment are examples of these ointments. They are pretty pricy, but they are good to treat minor wounds before bandaging. I have a number of tubes of antibiotic ointment which I store in a refrigerator to extend their shelf life.
Oral and injectible antibiotics are another story. In the U.S. these medications require a doctor's prescription. The only legal way to obtain a supply of these medications is to find a doctor that is sympathetic to your preparations and get him or her to write you a prescription for the medication. If this you find a doctor that will do this, I would suggest that you ask for some broad spectrum antibiotics like Ampicillin or Tetracycline. These are available in capsules that will stay viable for a long time if kept sealed and refrigerated.
Injectible antibiotics require refrigeration, so if the power goes out you only have a limited amount of time to use these antibiotics before they spoil. If you had to, you could keep them cool enough by placing them in a waterproof container and lowering them into a well. If you do acquire injectible antibiotics, be sure to also buy appropriate syringes, learn how to determine correct dosages, and learn how to give the injection.
Some people skirt the law by buying veterinary antibiotics. Veterinary antibiotics are available without a doctor's prescription, and you can find them on-line, or at pet and/or feed stores. Buying them is perfectly legal, but they are labeled for animal use only; so if you use them for human consumption it is technically illegal. For this reason I cannot recommend that you go this route, but if you want to look into it there is a lot of information on the inter-net. Veterinary Ampicillin costs around $30 for 100 250mg capsules. Veterinary Tetracycline in around $20 for 100 500mg capsules. Injectible antibiotics are also available as veterinary medicines but they have no dosage instructions for humans since they are not legally labeled for human use. If you are going to use injectible veterinary antibiotics do some careful research first.
Some people have allergic reactions to certain antibiotics. If these people ingest or inject an antibiotic that they are allergic to, they risk death from anaphylactic shock. So, don't mess with any of this stuff lightly. Best course of action is to stay legal and get a doctor's prescription and professional advice.