Can 2/3 drops of undiluted peppermint oil, and the same amount of undiluted lavender oil, cause any serious systemic effects when applied topically?

Depends.: If you are putting it on an open sore or cracked skin, it may not help and may make things worse. Any break in the skin increases absorption into the system of anything put on the skin. Also, a person can be allergic to either one and that is bad, too and this can have systemic effects. For the proper use of herbal products, make sure there is good, unbiased, ad-free research to justify it.