Hi, and welcome!
First off: if your water is green, by definition, your chlorine level CANNOT be good! Your pool store is completely mis-directing you.
Second: Right now, alkalinity is probably totally irrelevant--you have bigger problems.
Third: Alkalinity is relative. When you measure TA, it will rise and fall as pH rises and falls. Both Muriatic Acid and Dry Acid lower TA because of this.
Fourth: Low TA and high pH probably won't be helped by raising TA
Fifth: Your solution is going to be to shock, shock and shock your pool with chlorine, preferably bleach or Liquid Chlorine, until it's clear.

Now, before we can give you reasonable advice on amounts and levels, we'll need the following information which your pool store, with their "advice" probably gave you:
1) FC--Free Chlorine level. The good stuff that kills algae and sanitizes your pool. When you add chlorine, it releases this.
2) CC--Combined Chlorine or Chloramines. Chlorine after it's "used up". Smells like "Chlorine", and the ideal level is 0 (zero).
3) TC-- Total Chlorine = FC + CC. If we have any two of the three, FC, CC and TC, we can find the third. Ideally, TC = FC (because CC should be 0)
4) pH
5) TA
6) CYA--Cyanuric Acid, Isocyanuric Acid, aka "Stabilizer". This is like sunscreen for Chlorine. it's a two-edged sword as is slows the UV breakdown of chlorine BUT inhibits chlorine's sanitizing action. Ideal FC levels are based on the CYA level. Ideal CYA levels depend on your conditions and can range from 30ppm (probably best in Canada), to 80ppm if you live in Louisiana, like our moderator, aylad, does. But we need this.
7) CH--Calcium hardness or hardness. This is important to concrete/tile or other hard-side pools, but for vinyl and fiberglass pools, it's really only relevant if it's too high.
8) Any metal levels they've tested for.

We will also need to know what kind of pool you have: How many gallons/liters, material (vinyl, fiberglass, concrete), indoor/outdoor, brand and size (HP) of your pump, what kind and size filter, and if you have any extras: Heater (gas, electric, solar), water falls or other accessories, erosion systems (Nature2, etc) or inline chlorinator. Also what products do you chlorinate with? Any algaecides you've used? etc.