From what you have told us it doesn't sound like BEB, but by all means go to the BEBRF and get the names of Neuro-Opthal.'s in your area and get it checked out.
If you have a video camera, or a friend who has one, make a video of yourself while you are having the spasms. Otherwise you can't really see what is going on, because you can't see yourself blink. This will also be nice to take to your Dr. so S/HE can see what happens when s/he's not there!
A major symptom of BEB is facial-mask blinking, in which not only the eyelids but the brows and cheek muscles show signs of spasms. If you Don't get any of that, then it's likely just dry eyes. If you do see full facial-mask activity, it's probably BEB.
Welcome to the bb, Ruth, sorry to hear you are having this trouble. It sure sounds like beb to me - your symptoms are the ones I had when it first started. I was told it was dry eye as well - which it is, but its also beb/meige.
I would think you should contact the BEBRF and get their written information on the subject and see a movement disorder specialist for diagnosis. I don't know if Tears Naturale (the bottle) has a preservative in it - but you should really use a product that doesn't. I use Allergan Refresh Tears (it contains purite but that's ok) or Refresh Plus (individual doses) and at night I use Lacri-lube (its a bit messy but cover with eye blinds (wash them each day), and rinse eyelids each morning with a baby shampoo or a lid-care product. These eye drops, etc. should really help with the eye burning UNLESS that's a problem with your glaucoma - CHECK WITH YOUR DOCTOR.
Good luck and check back with us - there are a great group of people here to help and I'm sure more will answer your post.
June in Toronto (beb/meige)