I would not use a rotary epilator on your facial hair.
Where are you located? We may be able to offer some recommendations for a skilled electrologist. If you start now before things take off, which it sounds as if this is what is happening now, then this will be less of a struggle for you. Don't help stimulate facial hair by pulling out.
I always recommend electrolysis on facial areas. It plainly works. Cut through the crap and do this the right way. It will be less frustrating overall.
Dee
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Dee Fahey, R.N., C.T.
Licensed by the State Medical Board of Ohio for Nursing license and Cosmetic Therapy/Electrolysis license