Rosehip oil isn't just for your face. It's been shown to have anti inflammatory properties that can help reduce joint pain. It can be a good alternative for those who can't take NSAIDs. 

In addition to lavender oil being calming and something that can help relieve anxiety, a 2012 study found that inhaling lavender oil helped relieve migraine pain. It's also been found to have anti-inflammatory properties. 

Eucalyptus oil also has pain relieving and anti-inflammatory properties. A 2013 study found that it can lower blood pressure when inhaled. 

Suffering from IBS including abdominal pain? Peppermint oil can help with that (but consult your doctor first). It's also been shown to help relieve tension headaches when used topically. 

This article has 5 additional oils that have been shown to have pain relieving properties.