You will improve very quickly - I know it doesn't seem like it now, but I've found cycling gets exponentially easier very quickly. You will get there sooner, however, if you take some rest days when you're starting out. So if it's possible to take the bus or carpool a few times a week for the first month, I'd recommend that.

There are some things you can do to make a mountain bike zippier - putting slicks on, etc.

I suffer from allergies too, do you have an allergist? I was miserable year-round (grass/pollen in the spring/summer, mold and mildew in the fall and winter) until I was prescribed Flonase. Night and day, the stuff is amazing. My own mother didn't recognize my voice on the phone after a week of using it.