I used to get a lot of bouts of bronchitis (2-3 a year for 4 weeks at a time), and I used to have allergies. My understanding from the doctors that a combination of things are at play. First, when someone has severe nasal congestion (whether from allergies or infection), all of that swelling in those tissues constricts the blood vessels in the area. Blood doesn't flow as easily and so it tends to pool in the "vacant" areas such as the cavities under the eyes. Have you heard the term "allergic shiners"? Those are the black eyes present in so many allergy sufferers. I imagine (you should ask your doctor) that there may also be some pooling or accumulation of other fluids which could cause the bags. How long it takes to recover is something I can't answer. I also think the serious drying out that goes on could cause wrinkles, as could any swelling/puffiness that then starts to go away. Those drying-out skin cells are going to wrinkle and not plump up. I know it sounds contradictory - swelling/fluids vs. drying out in the same person, but the skin is your largest organ and it definitely can take a beating from a lot of things. And that's not even factoring in the effects of whatever drugs you were on.
I don't think there's a magical, topical cream that will make this better. I think you'll find that far more skin issues have to do with what's going on inside, in the deeper tissues of the dermis and below, than just on the surface in the thin epidermis that creams are treating. I think that is evident in a lot of skin conditions, from eczema to psoriasis and so on, which people try to treat on the surface but which really come from much deeper in. You probably didn't do much when you were so sick, so water levels, activity/exercise (which affect a bunch of things, including blood flow) and a lot more just really changed.
I know that my allergic shiners went away when I got rid of my allergies. No creams or concealers did as good a job, although I still certainly use a light moisturizer with SPF all the time. Cucumbers won't hurt you and may help (as much for the 10 minutes of rest you enjoy while they're on your eyes as from anything else!), but I would not put anything else on there that isn't designed for the face. I know you're kidding (sort of) about Preparation H but people come up with all kinds of suggestions that wind up causing more problems, especially if they get in the eye.