Waxing your upper lip is absolutely fine, on the condition you have no adverse reactions to the wax or that your skin is not too sensitive. It's a delicate area, so be careful using wax meant for use on other parts of the body (such as legs). Always do a patch test somewhere too, if possible, to see if you react with the wax. Disinfect the area with an alcohol wipe or equivalent after doing it to be safe.
Hair doesn't ever grow back darker if you shave/wax or whatever. What tends to happen is that it can often *appear* darker; the ends of hair becomes smooth over time. But it will never become darker! So remove hair as you wish!
If this is a persistent problem, I would highly recommend laser hair removal. It can take a few sessions to remove the hair, and it's a little painful when starting, but it seriously helps and is probably more cost effective in the long run! (Electrolysis would work too). If you opt to try out either of these, ensure the place you visit has a good reputation and always ensure you're given a patch test first. Laser is very safe these days, but it's best to test your skin's reaction to it. I thought I'd react badly because I have SUPER sensitive skin, but it actually wasn't an issue at all.
