If you're breaking out after tweezing or waxing try using an achohol swab to clean the area before you start and then a gentle cleanser after, and put on some gentle zit cream or medicated makeup on the area if you're prone to breakouts. Try to keep the area you've done as clean as possible. I usually screw up and go out and do something, then start sweating and, well, you know, here they come....
Try to keep you upper lip and/or face clean. It should help prevent or minimize the break out. Wear oil free makeup if you need to go out to help block sun and sweat.
I carry witch hazel wipes with me to cleanse my face while I'm out (I use the Preparation H ones since they are pure witch hazel. I know it sounds weird but they work.)
I been tweezing my upper lip for years so most of the hair is not coming back, but I am now getting fuzzy in other areas. sigh...........