You are going to have to go on a vape allergy elimination diet if you want to determine the cause. I think I may have said this on your other thread.
Try unflavored, no nic VG. Try all these things in a couple setups, one with a kanthal coil, one with a SS coil. You may also want to try cotton vs. rayon.
If that sucks, try very high PG next (still unflavored.) Then try adding in nic (salt and freebase) at varying proportions. If that starts to work, but some single flavors from various manufacturers and see how you get on.
It's a total pain, I've done my onw experimentation but that is what you may have to do. The in through the mouth out through the nose technique is also not a terrible idea the mucosal membranes in the mouth and nose can and do absorb nicotine.
Snus can also be useful if you can get it. I order directly from Sweden and you may be able to do that, but if you can try a small amount first somehow that may be worthwhile because shipping is expensive and you have to order in bulk.
The nice thing about snus is it contains a lot more of the minor alkaloids. You are losing the mouth to lung action but well, the alkaloids (for me) sort of compensate for it when I use it at work and am busy.
Harm reduction is said to be better than vaping (and I would think, especially if you have asthma.)
You could look for the thread, "What's under you lip, nose, etc part 2." it is the snus thread and those folks are knowledgeable. They can help get you started. You don't have to read the whole thread, just ask some questions and you will get help.
Best of luck,
Anna