trouble keeping chlorine- thinking we need to shock

Hi,
Great site!! New pool owner here--I filled out the info form. Just did our first test with Taylor kit with the following results:
.4 FC
.2 CC
90 CYA
120 TA
190 CH
8 PH

A little history, struggling for 3 months with suspected algae growth--vacuum clean, stuff comes back at same spots within 24 hrs or so, now its blackish dots on bottom of . Sick of pool company telling me to add this crap and that crap--last thing they had me do was an oxygenating shock and Pool optimizer (which I have since learned is borax). Despite doing superchlorinate with our SWG chlorine levels not coming up-which leads me to confirm algae?? Also had me do a bromine treatment a few weeks ago. I really think after studying your site I need to do a chlorine shock (with appropriate amount of bleach) following the best guess guidelines and monitor the chlorine until I don't loose more than 1PPM overnight. Am I on the right track?? Thanks!!