How can I get antibiotics for a tooth infection without having a doctor? Er and dentist are too expensive.

Cost vs benefit. I agree with most of the other answers. You will only be able to get an antibiotic from a licensed professional. Taking an antibiotic for a tooth abscess will not solve the problem but only mask it for a while. And when it comes back it may be worse than before and require hospitalization. I imagine that will cost even more.
Options. There are many options for treatment aside from dentists and the er, including urgent care centers and free clinics. However, you need to have a medical professional take a look, because things other than tooth infections can cause mouth pain, and not all of them respond to antibiotics. I'd suggest calling your local health department for possible free clinics and urgent cares in your area.
Tooth infection. Antibiotics will not cure a tooth infection. Antibiotics will only calm the symptoms temporarily. You need to see a dentist before the infection becomes worse. If you cannot afford a dentist, look for a free clinic that offers dental care, or a local dental school.
You cannot. In most areas of the country, you can find dental clinics that charge very low fees. Er's may also be able to provide treatment at very low cost or free..Try asking. You may qualify for public assistance/medicaid. Check with your state to see if they offer any state aid.
You need to see a Dr. Using antibiotics inappropriately can cause more harm than good. In dentistry, most antibiotics are only good for short term relief until the proper dental treatment can be done. An examination by a dentist should cost much less than a trip to most emergency rooms. Many cities have public clinics where you may find care more affordable.
PA's. You may be able to get one from places like minute clinics such as the ones at cvs where they have pa's or advanced degree nurses (i would call and check) that can write antibiotics. But this is only a short term solution and you need to find out/take care of the source of the infection ( if this is a dental problem) as antibiotics will not do that.
You Can't. While private dentist and hospital er visits may be more expensive than you can afford, you need to see a licensed doctor to prescribe antibiotics. For tooth related dental infections antibiotics may be prescribed to help control symptoms and lessen the infection. The only way to cure a dental infection is to treat the tooth that is causing the problem with either a filling, crown, or removal.