These are my two favorite all natural balms, which I mostly use on my nose when feeling dry. Well, eucalyptus does a nose good, sick or not.
Baume respiration (Respiration balm) by Biofloral
35ml in a screw-lid tin
It's shea butter based, vegan, 100% organic (certified), besides eucalyptus and peppermint contains plenty of other essential oils (lemon, cinnamon, lavender, rosemary, clove, thyme, silver fir etc) and feels quite strong, which I love.
Aromatic chest rub by Badger
21g / 0.75oz in a (nail breaking) press-on lid tin
This one is olive oil and beeswax based, feels less concentrated in essential oils and therefore more gentle. USDA certified organic. Besides eucalyptus and peppermint contains essential oils of ravintsara, tangerine, ginger, tea tree etc.
Both of them are quite hard to scoop out with a finger, that's why I use back of a nail if I want more than just a tiny bit. Once on skin, they melt instantly. They stand up to extreme heat without going any bad or changed. I don't believe they would do much as a chest rub but both are very usable as a lipbalm or wrist rub for aromatherapy.