Absolutely, I would not use it.
Containing a steroid (the "dex" in the name of the product), you could really exacerbate a corneal ulcer being present on the eye.
This is the first rule vet's are not supposed to break. We always do a simple eye stain test to know if any corneal scratch or injury exists first.
also, it sounds like he may also need an oral antibiotic as well.
I would only clean with some warm water, nothing else, until you consult the vet.
The most common eye tests performed by your veterinarian:
Eye Stain Test for Ulcers
Tear test for Dry Eye
Glaucoma Eye Pressure Test
Especially, with some blepharospasm (eye not opening all the way), well worth getting into a vet today.