Since none of us are your physician, there's no concrete way of saying what you are allergic to. Bodies can be a strange thing. I can tell you what I've experienced, and what I've seen others go through, and maybe that might help.
First, the local juice guy was right when he said the coughing would subside... I have seen this time and again, but it takes about 6 months. I was a smoker of 20 years, and when I started vaping, the coughing got worse. I did some research, and found out that a new vaper coughs for two reasons... 1) the vapor is denser. and 2) Your lungs start to heal, and that mucus has to go somewhere. It didn't take long for me to get used to the denser vapor, but the coughing got worse, and I was always clearing my throat.. this lasted for about 6 months for me. In the last two years however, I have rarely had the need to clear my throat or had excess mucus. my breathing is clear.
Now, as far as the allergy part... There's no telling what you're allergic to unless you go get an expensive allergy test. technically, you could be allergic to anything. However, I have noticed that more people are allergic to PG than any other ingredient. most of the allergies were slight swelling of the throat, and increased coughing. Most people would switch to a pure VG juice. It could also be some of the flavors you're allergic to. If I had to give advice as to how to best figure out what, is to try just VG and nicotine with no flavor. Try that for the first month. It won't taste as good since it has no flavoring.. it should just be a slight sweet taste, but it's definitely better than smoking. Of course you will still cough more due to your lungs healing, but that's the only way to find out. Also, try a different "juice guy". If you find that VG and Nicotine (Unflavored pure VG juice) are fine, then start introducing flavors if you'd like.