I have no insurance and 1 week on Penicillin. Jaw pain, swelling, and pain are still here. What is going on. I can't afford a dentist. Help (abscess)?

Infection. You have a major infection that is not responding to the medication you are taking. You will need to see a dentist to solve your problem. Financing or borrowing from a friend or family member may be necessary. Hospital residency programs may be able to see you at a reduced fee.
Could be. A persistent dental infection becoming a abscess is possible. With Obama Care you should be able to enroll or be seen urgently at an emergency room despite no insurance. Please get checked.
Jaw Pain. Unfortunately, sometimes when we have a serious situation such as you do we just have to go be seen despite the fact we have no insurance. Most of us don't have dental insurance. You need to get this taken care of as this potentially could be disfiguring and even life threatening. Explain your situation to who cares for you, they may be able to help with payments etc. Good luck.