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You should never use out of date medications for your pet.
If the puncture would is on the skin (outside of the mouth) you can clean it well with peroxide and apply some antibiotic ointment.
You can use aspirin for pain if the dog has no other health problems. My vet recommends that you give 5 mg per lb of dog every 12 hours with food. Don't give more than 3 doses. Your vet can prescribe a better antiinflammatory that won't cause as much stomach upset.
Let me know if you still have questions.