Yes, you need to chlorine. With a CYA of 45, you need to keep the cl between 3-6 all the time. Since you have dipped below that and also since you have 0.5 CC, I'd suggest shocking the pool again. Since you just added the CYA yesterday, I'd still wait until about Sunday or so and then retest for it again to make sure you have the final reading on how much is in there.
You can use a little baking soda to bump your alk up just a bit. Baking soda won't cause a big jump in your pH and even if it does come up just a little, that will still be fine. Add about a half a pound at a time and then retest after it has circulated for at least several hours. See how much it increases and then you can decide whether you need to add a little more. Aim for between 80-110 or so. Your calcium hardness reading is just fine.
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