Why are you afraid they'll recommend shots? Is it the expense or the idea of your child getting shots?
From personal experience, I can tell you that I had very bad allergies as a child, and this was back before there were many OTC antihistamines. Constant runny nose (which was embarrassing and uncomfortable), constant chapped lips due to runny nose, frequent headaches, burning eyes -- it was like walking around with a cold that wouldn't go away. My parents chose to take me to an allergist when I was 6, and I went through 6 years of allergy shots. I am SO grateful they did. It changed everything for me. Moreover, I'm glad they did it *when* they did it-- my dad went through the testing and shots at the same time, and while it helped, it never worked as well for him because he was older.
Yes, the initial testing was uncomfortable, but it was just two sessions, and the shots themselves weren't bad. In fact, the needle's so fine, the actual administration never really hurt. (Granted, they do itch afterwards for a while, or they did for me.) That's saying something, given that I was so frightened of shots, and hated them so much, I used to get hysterical and have to be held down to get one -- in fact, I once kicked an administering doctor in the crotch!
If the distance is the problem, keep in mind, you don't have to go see the allergist every time you get shots. In our case, my pediatrician was given the serum and we went to him to get the shots administered. When we ran out, the allergist would issue an upgraded serum.
The teeth grinding, I can believe. I used to do that when I was about your daughter's age because clenching my teeth was the only thing that alleviated the pressure in my sinuses. My dad did the same thing -- so much so that he eventually damaged the enamel on some of his teeth. Apnea's not likely at her age, and it would be a lot more expensive to go through a sleep clinic and test for it, anyway.
The problem with relying upon antihistamines is that many of them do have side effects, and some can increase risk of certain health problems. Plus, not all antihistamines treat the same things. As we have a family history of high blood pressure, I'm very glad I'm no. Too, you never know how they'll interact with other medications you may need to take.
Texas is utterly HORRIBLE for allergies, what with the cottonwood, live oak and cedar pollens. Please, consider the testing. If it's not allergies, you'll know it's something else, but if it is allergies, you can give your little girl some relief. She'll thank you for it later.
(And btw, my mom got me past my fear of shots by promising me a scoop of ice cream if I was a brave girl and didn't throw a fit with the shots. Maybe it was bribery, but it worked as a motivation, and I'm not at all bothered by needles now!)
Good luck. :)
P.S. Just saw your question about the testing. For me, they started with a scratch test, which is a series of small, round devices with tiny amounts of common allergens. The only discomfort is from the substances to which she's allergic, and those will itch a bit. Most of them probably won't react at all. In my case, they did a second round of those substances to which I reacted, but those were tiny injections, and there weren't many. That was it for me. Can't speak to the blood test, but I've had blood tests for other things, and those aren't bad, either -- would be even less of a bother for a little one than the scratch tests, I'd think.