Water does not appear to be filtered very well

The shock level you have to attain to kill off algae is dependent on your CYA level. With a CYA level of 30-50 ppm, your shock level is 15 ppm of chlorine, which you need to attain and then maintain, by testing and adding more chlorine as needed to get back up above 15 ppm, as many times as possible during the day. Hold that level until the green completely clears and until you can go from sundown one night to sunup the next morning without losing more than 1 ppm of chlorine. After you get it all cleared up and have no overnight chlorine loss, then you need to maintain your chlorine levels above 3 ppm at all times to keep the algae from coming back.

I think the problem is that you were never completely killing it off to begin with, so it just grew back when you allowed the chlorine levels to come down.

oh ok, thank you, is it better to add liquid chlorine when trying to raise the FC rather than bleach? I can get approx 3 gallons of 6% bleach for $5 or 1 gallon of 10% for $4.50. I have never used liquid chlorine and live 45 min from the nearest pool store so I have no ideal how much it costs or how strong it is....

Some forms of algae can be very chlorine resistant. The easy solution is simply to raise chlorine levels to compensate. Do this:

1. Add 3 gallons of PLAIN 6% chlorine bleach in the late evening. Brush the algae AFTER adding the chlorine.
2. Test the following PM; if the chlorine is ABOVE 15 ppm, skip the dose. Otherwise, repeat add 2 gallons of bleach.
3. Brush every other evening, and continue with the 2 gallons, if under 15 ppm, EVERY evening, for 4 days after NO trace of algae and NO trace of green is left.
4. Do NOT turn the pump off during this period; clean the algae that won't filter AFTER 110% of the algae is LONG dead.

update: that was my problem with the green coming back. Once I held the chlorine at 15ppm for several days, then vacuum to waste thru pump/filter. Then turn off pump for 24 hrs for the fine particles of algea to settle and vacuum to waste with a 5 gallon bucket, not thru the pump/filter. This was the end of my green battle! :) My pump is still running, we still bang on it with a rock if it wont turn on and it starts pumping.............However it still does not seem to filter out anything other than leaves or large bees. I still have to vacuum thru filter with someone holding pantyhose or a knee sock (or both) over the return to filter out everything except the small particles of dead algea. For the record, NOTHING will filter the tiny bits of green algea. I held every type of fabric I could think of over the return to try.......green water blew thru everything. Silk filtered it the best but the water had such a hard time getting thru the silk fast enough that it would fill up my fabric "bag" and eventually burst at the seams or if not then even my strong hubby couldnt hold it over the return. Even for as long as he could hold it on there, green water would seep out anyway. I ended up putting floc in the water, letting it filter for the day, then turning off pump for 2 days and then vacuum to waste with the 5 gallon bucket method. That was the cleanest and clearest I got my pool all year. Its still not crystal sparking clear but all the green is gone, you can easily see to the bottom. It has an over all clear look but when you look very closely or when a light is in it at night you can see tiny bits of "something" floating in the water. I would say it was pollen but last year (the first year) it never did this. I still think my pump is too strong for my filter and when this one goes out I plan on replacing it with a smaller one even though all the pool places still recommend one this size for my pool. Thanks for all the help, we finally got the pool under control though it was disheartning how many swimming days we lost, not to mention the higher water and electric bill with all the vacuuming to waste and refilling.......sigh, but now I am more experienced;)

CYA scale is not linear so if it is near 30 ppm just call it 30 ppm. For the TA (and CH test) you want to keep adding drops until one more drop produces no more color change and then do not count that last drop. For example, if the test started changing at 7 drops, turns red at 10 and an 11th drop produces no further color change then don't count that 11th drop. Your TA would be 100 ppm. Also, just because an vinyl pool does not NEED calcium does not mean you do not need to test for it. High calcium levels can be problematic for ANY pool and evaporation will concentrate calcium over time. You probabloy don't need to test it more than once a month (unless the TA "mysteriously" drops or the pool get cloudy and it is not algae--however, in these cases it is usually too late and if you had known the CH before hand you could have taken corrective action BEFORE these problems).

AS far as filtering out living algae, you are correct. It cannot be filtered out. You have to kill it first.

As far as bleach vs. liquid chlorine, the only difference is (sometimes) the strength (and therefore, the amount needed to achieve a certain ppm of chlorine in the pool). Laundry bleach is sold in 3%, 5.25%, 6% and lately 8.25% strength. Pool chlorine (which many pool tech call "bleach" because it is!) is sold in 6%, 10% and 12.5 % strengths, with the last two most common. 10% is usually sold in one gallon jugs and often spends a lot of time sitting in a warehouse so it might not be 'full strength' when you buy it. 12.5% is usually sold in refillable carboys and, if bought from a supply that sell a lot, is usually fresh. In many parts of the country 12.5% pool chlorine is a more economical way to chlorinate than bleach is but you have to do the math first. Laundry bleach is usually going to be fresh if you buy it from a high volume retailer like Walmart. Both bleach and pool chlorine are exactly the same, sodium hypochlorite.