You have two separate problems. The very high TA, assuming you are measuring it correctly, can lead to calcium carbonate scaling of pool surfaces. That's why the pool store is concerned. A high TA can also lead to the pH rising which increased the possibility of scaling as well.
The other problem is algae which most likely is coming from your continued use of chlorine sticks which are probably Trichlor. For every 10 ppm Free Chlorine (FC) added by Trichlor, it also increases Cyanuric Acid (CYA) by 6 ppm. So your CYA level may be very high and this makes even high chlorine levels ineffective if the CYA is very high. If the FC drops below 7.5% of the CYA level, the risk for algae grows.
First of all, you need a good test kit so you can make sure your readings are correct. The best to get is the Taylor K-2006
or the TF-100
with the latter kit having more volume of reagents so is comparably priced per test (you can read about the difference in these kits here
. To learn how to maintain your pool, I suggest you read the Pool School
. You need to test your CYA level and probably need to do a partial drain/refill to lower that level and then shock your pool with high levels of chlorine -- higher than what your current test kit will probably be able to measure (which is why you need a good test kit -- to accurately test multiple water parameters including chlorine using a FAS-DPD chlorine test kit).