Weird streak on upper lip

Hi,
I've been having a few problems that might  be related, but I'd like advice on this lip thing for now. I've had a red vertical streak (looks almost like a paper cut, but doesn't bleed) on my upper lip, close to the corner but not on the corner.  The streak gets redder/more irritated at times and burns a bit. It usually turns back to normal within hours and especially if I apply menthol chap stick. However the red streak remains, it never disappear completely.  I've been having this for weeks and weeks, but it seems to be getting worse lately.
Can anyone tell me what this might be? :-/ I'm puzzled