Lavender is known for being soothing for fussy babies especially when they are sick. I personally use lavender oils when I am not feeling to good and can't sleep that well. It usually puts me straight to sleep.
Eucalyptus, to me, is the best in terms of treating colds. It lets you breathe easier, and lessen any aches and pains. Eucalyptus is also usually used to relieve other common cold symptoms such as coughs and sore throat.