If you've been diagnosed with blepharitis it is a very strong bet that it is the cause of your burning and eye watering. Allergic conjunctivitis certainly can play a role in those symptoms as well, but if you're not experiencing significant eye itching, I wouldn't suspect that to be the case.
I noticed you've tried scrubbing your eyelids for blepharitis. I think this is a good thing to do. I would do it as part of a daily regimen of morning hot compresses (5-10 minutes, as hot as you can tolerate without burning your skin, massaging your eyelids while they are on there) and then doing eyelash scrubs. What works well is if you take 4-5 drops of Johnson's baby shampoo and put it in 1/4 cup warm water; then use a qtip dipped in that solution and scrub on the eyelashes of all 4 eyelids for 15 seconds per eyelid, then rinse the solution out. The thing that is important about this therapy is it needs to be done every day for it to be successful. Also, it does take about 3-4 weeks of doing this every day before you may notice a significant effect. Because it takes that long of doing it every day before a significant effect is noticed, I recommend using artificial tears 4x/day in both eyes consistently every day until you've been doing the compresses and lid scrubs for about a month. After that, you can start backing down on the tears to as you need to, but if you start by using the artificial tears only when you feel like you need them, they usually don't work for any longer than a few minutes after placing the drop.
These are baseline treatments for blepharitis. If you're doing this faithfully and yet you're not completely better, you may require an antibiotic/steroid combination to eliminate some of the inflammation in the tears and some bacteria that like the inflammatory environment in the tear film.
The reason it blurs when you blink is because the layer of tears in front of your eye (tear film) is not healthy because of the blepharitis and it is this tear film which is responsible for clear/fine vision. A disrupted tear film like yours causes you to have blurry vision from time to time that changes upon blinking and is worse with computer work, reading, watching TV, or driving (all activities that keep your eyes open for longer periods at a time).
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