If you have had hundreds of allergy panels done in the past, then this is a pretty good indicator that you are almost certainly not allergic to a particular thing. Meaning, it is very unlikely that the rash and the cracking of your lips is caused by exposure to something that you encounter while traveling.
On the other hand, I think it is quite possible that you simply have perioral dermatitis or eczema
. This is a very common condition, eczema, which is an inflammation of the skin of unknown cause but that is usually worsened by stress and fatigue. In other words, it might come out when you travel simply because the change in your routine upsets your equilibrium and brings it out. The portion on your lips is probably also worsened by lip licking.
Treating eczema requires keeping the skin and lips well moisturized at all times with a thick occlusive ointment (such as hydrolated petrolatum). As you have done in the past, a steroid cream can be used to treat more troublesome red and itching spots, although you should always be careful about using a steroid on the face for more than 1 or 2 weeks.
Talk to your dermatologist
if you still have questions.