People give a lot of potentially dangerous things to their children for teething pain, either due to lack of information, or out of pure selfishness. I personally know a couple who used paracetamol syrup almost every night when their son was teething, just to make him sleep through the night. Even though paracetamol is considered relatively safe, I find it cruel to medicate the child for the personal benefit of not having to get up at 3 am.
Types Of Painkillers
Over the counter drugs — They're able to decrease minor pain associated with conditions such as fever, headaches, colds, flu, toothache, arthritis, and menstrual cramps. There are several types of OTC pain relievers, the most popular and widespread being acetaminophen and ibuprofen. Acetaminophen (or paracetamol) is an active ingredient found in numerous OTC medications as well as prescription medicines. Ibuprofen is also used to relieve fever and minor aches and pains. 
Prescription medications — Prescription painkillers such as morphine, codeine, oxycodone, or hydrocodone — called opioids — are associated with painful drug withdrawal. If used a lot while pregnant, it’s almost a definite that a baby will be born premature and addicted. 
1. Avoid Giving Opioids To Your Baby
Mrs. Winslow’s Soothing Syrup, the remedy that contained 65 mg of morphine in each fluid ounce was widely used to quiet restless children in the 19th century. This “medicine” reportedly killed numbers of babies. One would think that the situation is better nowadays, but no — opioids killed 28 thousand people in 2014. 
It’s very important to not use Aspirin in the treatment of teething pain, increased temperature, or any other ailment in children. Aspirin is fine for adults, but in children it can cause a condition called Reye’s syndrome, a rare but serious neurological condition that causes swelling of the liver and the brain. 
Reye's syndrome occurs mostly in children who recently had a viral infection, such the flu or chickenpox. Taking Aspirin as the treatment for such infections can increase the risk of developing the illness. The exact cause of developing Reye's syndrome is still unknown, but some studies have found that 90 to 95 percent of patients in the US had Aspirin during a recent viral illness. Since there’s not much research on this connection and it can’t be confirmed that a virus is causing these symptoms — never give Aspirin to your baby for teething pain or any other reason, unless a doctor advises it. 
As Reye’s progresses and affects the child’s brain, she may become delirious, hyperactive, agitated, and confused, have an unusual posture, and have convulsions. Without the right treatment, a baby can slip to a coma, or even die. Aspirin has been banned for use in children under 12 in the United Kingdom. Experts recommend avoiding Aspirin altogether in those younger than 16 years (some even suggest 19 years of age). 
3. Dipyrone (Metamizol)
Experts suggest that all brands of dipyrone/metamizole (such as well-known Analgin or Novalgin) should be completely avoided in the treatment of pain and fevers. Even though dipyrone-induced agranulocytosis was considered quite rare, it’s a potentially lethal reaction to the drug.
4. Lidocaine viscous
Besides its usage in the treatment of teething pain, lidocaine was used to treat ulcers in the mouth region, and to reduce a gag reflex during dental procedures in children. Swallowing too much lidocaine can cause seizures, serious brain injury, and heart problems. According to the FDA, overdoses have caused infants being hospitalized or even dying, with 22 reported cases of serious reactions in 2014. 
5. Alimemazine Tartrate And Paracetamol Mixture
The Medicines and Healthcare products Regulatory Agency (MHRA) issued a warning that a mixture commonly used to ease teething pain, containing alimemazine tartrate and paracetamol, is contraindicated in children under the age of two years with a potential for adverse effects. 
Alimemazine is not even approved for use in humans in the US, and in Russia it's used to treat anxiety, mood and sleep disorders, and even depression.
Be Careful Even With Paracetamol And Ibuprofen
They’re both considered relatively safe  in the treatment of teething pain, but it’s best to turn to more natural ways to relieve teething pain, such as gum massage or a wet washcloth, and use medications only if necessary.
What is considered unsafe is routinely alternating or simultaneously using paracetamol and ibuprofen. Despite the recommendations from the National Institute for Health and Clinical Excellence and the American Academy of Pediatrics to cut this practice, it is still around in many families as a part of teething pain management in infants.