Tea tree oil is the 'go to' for applying to skin afflictions, to help prevent infection and assist healing, and it is also good for respiratory ailments, and assists the immune system in it's job of defending the body.
And if you're only going to have one essential oil in the house, lavender would be a perfect choice because it too has amazing skin healing properties and is good for the respiratory system, but it also has the added advantage of being great for assisting sleep through it's calming, relaxing effect, and can also improve mood. Plus lavender essential oil is the most awesome thing for inflammation, redness, heat burns and sun burn.
These two essential oils are fully recommended for adding to your natural first aid kit. They are both a testament to the power of nature's ability to heal.