Hi Emitayak, as everyone has been saying, there are so many variables here it is difficult to pin point. Here are a few observations and conclusions that I have made regarding the subject, hope these are of some use:
I find that with the acidic juices, I get cracked lips or fingers from handling or tasting the juice sometimes. Some of the sweeter tobacco juices or the fruity juices are likely to contain acidic flavour bases. These bases are no more dangerous than eating some fruit or drinking a sugarfree soft drink. PG and VG are what I would call mutual solvents (exhibiting solubility in both water and oil). As they are soluble in oil (to a certain extent) they will solublise or dissolve it. Your natural skin oils (collectively known as sebum) will therefore be dissolved by the PG or VG. If you get it on your skin, the VG or PG can 'wash away' these oils and when you wipe off the PG/VG you are effectively taking some skin oils with it. A bit like if you get petrol or nail varnish remover on your skin (it will appear dry when you remove it) - tell me how I know that lol
That is a very extreme example though, but it is the only everyday stark example that came to mind. Petrol and nail varnish remover are very aggressive oil dissolvers in comparison to PG and VG, they are also in a different class legally (flammable/irritant/harmful etc...).
There is really nothing to worry about here (nevertheless, good to have bit of a chat about it), as the solubility of your skin oils in PG or VG is not very significant in comparison to petrol or other more aggressive solvents. Also, your skin is not comming into contact with much PG or VG (unless you are packing or bottling the stuff). Simply make sure you moisturise regularly to maintain fairy soft skin lol

Loads of things that dry out your skin everyday are considered more dangerous, for example UV light lol
PG and VG are not usually considered allergenic, pretty much the opposite really, infact their 'hypoallergenic' (not likely to cause allergic reactions) property is one reason why they are so heavily used in cosmetics. Some people have been known to be allergic, but if you have only experienced the symptoms that you talked about, I would highly doubt that you are allergic to them at vaping doses. Drawing the vapour into your lungs would illicit a response much worse that a chapped lip if you were.
Hope these ramblings give you a bit more info on the subject, very interesting to think about indeed!
Keep on vaping!
Cheers
Pete