Your pH and alk are both ok but if you are going to use trichlor tabs or dichlor powder, you need to keep an eye on pH as it will drop. Having said that, right now while you are fighting algae, trichlor pucks are not the way to go. You cannot shock a pool to needed algae-fighting levels with tabs.

I have a feeling that you are going to find that it is going to take a LOT of bleach. Did you have a CYA reading when you closed the pool? Pools that close with a CYA level and open to none and have a high CC typically have the same scenario going on that we frequently see in the spring. Bacteria "eat" CYA over the winter and "poop" out ammonia. It takes a lot of bleach to break down the ammonia. Keep hammering your pool with bleach and try and keep the chlorine high. Also, run your pump 24/7 and keep an eye on your filter pressure.

After you get your pool cleared up, you can bring the CYA up.

Good to see you back this year!