Wow, I just went through this with my doctor (s). 3 doctors have told me that my stress has been making me sick. My immune system has been run down lately. I came down with Shingles and have had GI problems too. Yes, stress/anxiety can lower your immune system. Your body is releasing cortisol constantly and it triggers chemical reactions in you body that affect you Immune system. You can get sores in your mouth, sinus infections, ulcer, etc...I have made myself sick over the last 8 months. I'm still trying to work through my anxiety (hypochondrism) and it's hard but do-able. Excercise, good food, rest and keeping you stress under control can bring back you Immune health. Multi-vitamin also is a must. Take an anti-depressant instead of drinking if you have to. It is safer for you and the ones around you. Don't drink anymore, this is causing more stress for your mind and body!!
Poor sleep habits can increase stress and fatigue. I'm not sure if when you refer to "time zones" if you mean flying from one to another, or just the time change 2 x a year. Flying into a different one can interfere with your sleeping, adding to the problem of fatigue and stress. I have never believed that moving our clocks an hour forward or back could possible have any affect on us, but I read where it can and does affect some people. The alcohol causes anxiety, poor sleep and many other problems. You need to decide if you are drinking to forget or deal with things and if so seek help for this. Drinking only allows you to forget for awhile, then when you sober up, reality hits you right between the eyes. Thus, drinking more helps....a very slippery slope into a dark hole! Air conditioning or even cold air does not cause the flu or colds. You have to come in contact with someone to get the flu or catch a cold. Hope this helped. Take care!