I too would suggest seeing a pulmonologist and an allergist.
If neither of them can help you, a psychiatrist at that point might be helpful. If you are not able to find a valid medical explanation, which can take some time and may cost you some money, then what is left is a psychosomatic reaction.
What leads me to the latter is that you said you were around vapers "outside" unless they are blowing the vapor directly at you, (which you can certainly ask them politely not to do) or alternately, you could ask your employer to station you where you are not NEAR vapers, honestly, if you are doing some sort of outdoors work, like you work on trimming one bush and the vaper(s) the other, well, I am here to tell you that if you have an allergy (and I'm not saying you DON'T) the amount of possible inhalation of the offending substance would HAVE to be on the order of parts per million.
This is not necessarily unheard of, some kids are so allergic to peanuts that ALL of the offending peanuts must be removed from the school, and it's a real effect the kid can go into anaphylactic shock and die. Your extreme reaction to vape does NOT lead me to believe that "experimenting on yourself" would be at ALL wise.
I would go see your PCP, and explain to him again that you are having a severe reaction and get your REFERRALS. In the meantime, if he is not a jerk, he could certainly write your employer a note that you are currently experiencing an as yet unknown BUT SEVERE reaction to vape, and that you cannot be around vaping period. This would in essence be a "disability" and thanks to the ADA your job should be protected which either means getting the vapers to vape elsewhere, and when you are not around, so your health is not being harmed (if it's a health thing). Then go see the allergist and pulmonologist and get it figured out.
If and when ALL medical causes are ruled out (and they may not be, you may find you are severely allergic to a component in the vape) but if no medical cause is found, then you'd need to figure out how to deal with a psychosomatic reaction (which can be equally debilitating) etc.
I am more or less inclined to believe you, you sound like a reasonable enough person and I can't see too much motivation to LIE about this stuff.
If you are in fact making it up, (which again, I somewhat doubt) well, you'd actually be in better shape medically, although it doesn't speak well of your ethics, and I assume you would get what is owed to you, at some point. But right now I believe you actually and I hope you can get it sorted out. Etc.
Anna