I've always been a tad hairy - family thing. calmed down when preganant and while BF, but when DD slapped the boob away (11 months)the hairs on my face went mental!!!!! Must be hormone related, but the Docs won't take it sersiously! Don't shave, a good pair of tweezer will help with hairs on chin, but will need to used daily. A small pair of scissors may help with upper lip, but it does depend on colour of hair.
Any wax strips (for face) will do, best to do after period. TBH it does smart, but not for long. don't do it before you go out as you'll end up with red marks. when i was braver use to like the wax that you melted, as it felt nice when you put it on your face, but can be tricky to take off. You wouldn't have to do it too often, if you use tweezers to help maintain inbetween.
there are creams you can use, similar to stuff you put on legs, but I had to stop using these as they didn't last long, and it never felt right afterwards.
A friend swears by electroysis - but you have to let it grow, but does say it's permenant. You can also get laser treatment - pricy!
Do go to the docs, but please don't worry there are plenty of hairy ladies out there. Hoping to get pregnant again - so face feels normal again.