The persistent mustache, any advice?

I have a persistent mustache that I hate. The rest of by body hair I'm ok with, but this mustache was sent from hell to torture me. I have very dark, thick hair so even when I shave it real close it is still slightly visible and grows back to little stubbles by the next day. Anyone have any tips on dealing with this?? I used to wax but by the time the hair got long enough for the wax to actually work it was really visible. I love my body, don't get me wrong, but I would be way better off without this damn mustache. Shaving sucks and it always gets red and upset, even if I use shaving cream. Any tips are appreciated on better hair removal or ways to disguise it (I've used cover-up but it looks unnatural, plus I wear no make up at all most days).

Related story: the work I do gets my face dirty sometimes: soot, dust, dirt, etc. Whenever I ask friends if I have dirt on my face they always say I have a dirt mustache, and when I try to clean it they say it's still there. I've realized this is my actuall mustache stubble. Ugh