My dizziness comes and goes. I've had it for about a year now, caused (I guess) by fluid build-up in my ears when my nose and sinuses can't drain correctly. Sadly for me, the spells are getting worse and more frequent and are hard to live with. There may be sinus surgery in my future, but I'm hoping to find another solution first.

I never would've thought that allergies would cause dizziness, but, yes, apparantly that is that case. Sorry you're having to go through that. It is no way to live.

First thing you need to do is narrow down the source of the symptoms. Maybe it's not random. Keep a diary. When you're sneezing or dizzy, write down what happened and where you are (home-which room? at work? outdoors? indoors-where? car? near a window? near something blooming?), what you ate that day and when you ate it, what you used on your body (personal care products are loaded with allergens). Did you wear something freshly washed or dry cleaned that day? (detergents and cleaning products are loaded with allergens). Were you near something or somebody when you had the symptoms? This just started recently, so what is NEW around you that showed up when the symptoms started? If you can take diphenhydramine, do so and see if the symptoms go away....if they don't, then it's probably not an allergy. If they do, take a look at your diary and see if you can find a pattern that ties something new in your surroundings to the sneeze.

BigSur said it very well. Try to find the cause. You say your allergies are new. Did you move? Did you start a new job? Did you, or a neighbor. get a cat? Explore your surroundings, try to find the root cause.
I treated the symptoms for decades. I had 6 years of immunotherapy, from 1977 to 1984, that started with skin tests on my arms to find what allergens triggered my sinuses. My doctor acted surprized at how large the bumps got. He said he had never seen any that big. I had nasal surgery for a deviated septum in 1998. Those both helped but basically, I suffered from allergies from about 1965 till late 2009.
I said "triggered my sinuses" because I discovered the real problem late last year. While I was on the weight loss program, I did not eat any bread, macaroni etc for months at a time. It occured to me that I was allergic to wheat. We had pizza one night and I sat up till midnight with a sinus attack. days later we had pancakes for dinner (with organic, whole wheat flour) and I sat up till 1 am with a sinus attack. I quit eating wheat and no longer have sinus allergies. I couldn't tell you if it is the gluten or whatever. What I do know is, if I don't eat wheat a box of kleenex lasts me for 6 months instead of 2-3 weeks. My record was 3/4 of a 160 count box in 1 day. That was 2 years ago.
I recommend testing for food allergies, either by a doctor or test yourself simply by elimination. You may have to eliminate sosomething like wheat/gluten for 2 or 3 months to see a big change, so obviosly, it is a very time consumming method, but at least it is cheaper than paying your own way at the doctor.

This would definately be Rhinitis related.... its more then likely outdoor allergies. A decongestant is all that helps with these symptoms. But shouldnt be taken everyday. May need to see an allergist to get a more regular daily treatment.
Hope this helps as I can relate for sure.