I got a filling done that caused an infection. Is there temporary relieve until I can get back in to see the dentist? The pain is fairly significant.

Use Antiinflammatory. For pain control at this time, the use of a medication like Aleve or Advil would help if you are not allergic to this kind of medication and have normal kidneys. If these medications are a problem for you the use Tylenol (acetaminophen) but do not exceed 3000 mg in a day. Call your dentist and see if he will start you on an antibiotic.
Yes. A good thing for short term (1-2days max) for pain relief = combo of 800mg Ibuprofen and 1000 mg Tylenol (acetaminophen) (max dose 4000mg per day) every 6-8hrs, but for the infection the best thing is extraction if unrestorable, root canal if is restorable and antibiotics.
Wrong. The filling did not cause the infection. The tooth was infected, the infection removed, and a filling provided to replaced the damaged tooth material. There may be nerve damage from the infection or perhaps the tooth is fractured. Get back to see your Dentist immediately. Until then cold compresses, Ibuprofen exactly as directed on the package, and try to sleep sitting upright.
Deep restoration. There is a difference between a deep filling that resulted in the death of the tooth nerve tissue (and possible infection) and a deep filling that is painful and sensitive to cold. An infection needs to be treated with antibiotics, sensitive tooth with OTC pain meds. The sooner you can be seen the sooner you can be seen the sooner you will feel better. Call your dentist to discuss.
NSAID OCT or Tylenol (acetaminophen) According to your symptoms you have typical inflammation of the nerve and need root canal treatment. Once you have irreversible pulpitis, there's no reversible cure and visit to your dentist is warranted. Take NSAID OCT or Tylenol (acetaminophen) for pain control.