adding calcium chloride and sodium bicarbonate at the same time can cause the pool to turn cloudy as it might precitpatate calcium carbonate into the water.
Clear, green water after a heavy shock might be an indication of copper in your water. Get your water tested for metals in addition to all the other tests that Watermom said.
Have you ever added any algaecide to the pool? Many of them are copper based. Also some trichlor tabs now contain copper. They promote them as 'dual action' . Do you have a heater with a copper heat exchanger? That can be another possible source of copper, escially if both your TA and CH levels were too low as the pool store implied by having you add calcium and bicarb to your pool.
The other place to look for copper would be your fill water.
Once copper has been added to your pool it can stay there for years only to show up when you least expect it!