I maintain FC=7-9 with a cya of 50 - 60 and still get the beginning of visible algae in low circulation areas of the pool even with 0.0 CC.
This is your problem more than anything else.
Just because you test your FC and find it at the correct levels does not mean that this number is the FC
everywhere in your pool. In low circulation areas it is easy for algae growth rates to exceed chlorine kill rates. As a personal example, I have a waterfall with a partial stone ledge that is submerged in only 2" of water. There is a rock embedded in the wall near it. Right at the water line where the mortar joint is holding the rock in place I get a very tiny patch of green. It's standard green algae and it's able to grow because the FC in that area is lower than in the bulk of the pool water. However, it stays confined to that tiny little patch and never grows any larger.
Improving circulation and maintaining the correct FC/CYA ratio is the best way to avoid algae of any kind. As I said, the 40% was chosen using two constraints - making the amount of chlorine high enough to totally overwhelm the algae growth rates BUT low enough so as to not damage liners or plaster colors. There's nothing especially magical about 40%. One could use 60% or 80% and get even faster kill rates. One can use 20% and get lower kill rates. 40% was chosen simply to strike a balance and allow a pool owner the ability to clear a pool in a reasonable time frame.
In fact, if a pool for some reason bottomed out in FC and got a little cloudy, 40% might not be necessary at all. For water that is a little hazy from having too low a chlorine level, 20% FC/CYA ratio could easily cure it as well. Again, 40% was chosen for efficacy, safety and consistency. TFP does not want to teach people, like the pool stores do, to just blindly throw in whatever amount of chlorine and hope it all works out. Consistent application of chlorine both as a cure (SLAM process) and as a preventative maintenance measure (testing and maintaining daily chlorine levels) is what we teach...not the pool store "
dump and pray" methodology.
As for shocking weekly, yes you can maintain a pool that way. However, it is typically more costly to do so. Consistent levels of chlorine over long periods of time uses less chlorine overall than allowing FC to fluctuate and then blasting the pool with shock. Would you rather drive in a car where the driver maintains a consistent 40MPH or a driver that slams on the gas, goes 0-60MPH in 4 secs and then slams on the breaks when he reaches a stop sign? Which way of driving is better for the life of the car and the passengers inside??
As for burning eye, these are the three main factors -
1. pH outside the 7.2-7.8 range
2. CCs too high
3. Rubbing your eyes too much - you should blink when you come up from the water, not rub your eyes.
