For upper lip work, Icy Hot with lidocaine and menthol is worth a try. My clients verbalize that it is very helpful.

Walmart's price is good:

https://www.walmart.com/ip/Icy-Hot-Lidocaine-Cream-2.7-oz/51258774
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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
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ELECTROLYSIS FAQ'S:

British Institute & Association of Electrolysis

http://www.electrolysis.co.uk/?page_id=16