S. -
Be assured...this is actually pretty common when moving cross-country. I didn't experience it so badly when I moved here from North Carolina 3 years ago, but it hit BIG TIME when I moved to North Carolina several years back after spending my entire life in California.
In California, I was a business traveler (west coast and even occasionally overseas) and always pretty healthy, so I figured I had pretty good immunity established. Then I moved to NC. I was sick that ENTIRE winter. It took 3 courses of increasingly stronger antibiotics (that messed my digestive system up big time) and 2-3 months to get rid of my bronchitis, plus I had upper resperatory stuff & miscellaneous other stuff. I was miserable!
My boss, who had moved to NC a few years before me after spending most of his life in Illinois and was also a business traveler told me that he had the same experience when he moved to NC. And both of my kids have had similar issues when we brought them to the U.S. as international adoptees.
It has been explained to me that out of the thousands of cold viruses, each area has some more than others. So you develop immunities to the ones that are prevalent in your area, and only tend to catch the new ones that come in each year. When you move to a new area, particularly one with a different climate, you tend to catch not only the new bugs for the year, you get all the ones that have been around that area for a while but that you aren't immune to yet.
It took me a bit over a year to develop my immunities in NC so I was basically healthy again - not catching every bug that came through. It took my kids about six months and twelve-sixteen months, respectively, to develop their immunities here in the U.S. so that they weren't sick all the time. So take heart, you should come out of this OK.
Now, allergies can be a different matter. If you're allergic to stuff here that wasn't where you were before, that could be a longer term issue that you should discuss with your doctor.
Hope this helps.
B.