Hi summersun,
Yes, that can happen.
Do you apply the oil directly to your skin?
You might want to try and mix it with some massage oil, with a blend of Sunflower, apricot, jojoba and vitamine e massage oil. I have sensitive skin, and I find a few drops in the massage oil makes all the difference.
Some essential oils are more powerful. Bergamot, cedarwood, cinnamon,marjoram,peppermint,rosemary,
sage, are all very powerful oils, and should be used in very low dosages.
Try sticking to chamomile,frankincense,lavender,neroli (very nice), patchouli,rose,and sandalwood.
There are many more oils to choose from. Try adding 3 or 4 drops in your bath water can be very calming, depending on what you choose.
Hope I was able to help. Please feel free to ask me more if need be.
Peace and Love Carlee