There are (literally) hundreds of potential allergens and other toxic chemicals in cigarrette smoke which can cause skin reactions like you describe. I’ve studied far more Chinese Medicine than Western Medicine, and the link is clear within that system, but doesn’t mean much to most people in English. (Stagnant Qi and Toxicity of the Liver causing excess heat and dampness, if you really want to know. Also Lung Heat and excess yang, which expresses on the skin in redness and swelling.)
Really, I’m not sure what you’re asking. Could the cigarrettes be causing your skin problems? Sure. But you already knew that. Anecdotally, my large group of smoking friends (and I was one of them) all recognize the link between smoking and bad skin. Acne, dryness, redness, swelling, irritation - all exacerbated by both the chemicals in smoke and the actual heat and drying effects of the physical smoke itself. Smoke is hot and dry - neither of those are things that skin likes.
Is it an allergy that allergy medication can alleviate? Probably not. Allergy medicines are usually antihistamines, and this probably isn’t a histamine response the way hay fever is. Histamine responses are earmarked by mucus production or itching. This is a physical and chemical irritation of the epidermis. But you already knew the antihistamines aren’t working. It could still be an “allergy”, but probably not exclusively. Most likely it’s a combination of evils.
So yes, the problem is very likely to be the cigarrettes, but no, it’s probably not an allergy the way you’re thinking of it. Allergy pills are not likely to help. Quitting smoking will. In my experience, a dedicated regimen of herbs and acupuncture might help, or it might not. If you’re a heavy smoker, no way. There’s only so much “health” you can add to the equation. If you’re not willing to eliminate the “unhealth” then it can’t overcome that challenge.
As for the “you are addicted” pile-on that’s brewing, it’s important to remember that cigarrettes are multiple level addictors. Yeah, if you’re going for days without one, you’re probably not physically addicted. You may not even be psychologically addicted (needing one for purely mental reasons). But there’s another level of addiction, which I think only former addicts really recognize: social addiction. You sound a lot like me when I was smoking, where you’ll go days or even weeks without smoking, but then you hang out with smoker friends again, and find yourself buying a pack on the way there or bumming off people all night. Smoking is a social thing, no doubt. It can give you something to share, something to distract you when things are uncomfortable, something to occupy your hands, something to gesture emphatically with. (How many times have you finished a great conversation and lit up as an exclamation point at the end? I did that all the time.) Plus, of course, the chemical cocktails of nicotine and alcohol or nicotine and caffeine are wonderfully yummy and orgasmic.
My point? You can be physically, psychologically or socially addicted to smoking. I believe you that you’re not the first. But I strongly suspect you are the final.