Yes, you can just use plain, unscented bleach as your source of chlorine. Most of us use generic Walmart bleach.
We don't trust test strips to give accurate results though. We think that everyone needs a good test kit. The one we recommend is the Taylor K-2006 or 2006C which you can get through the test kit link in my signature below. Try and order it early in the morning while the seller listed is Amato Industries. Sometimes they sell out during the day, but usually restock overnight. Some other sellers don't sell it for as good of a price.
Since the kit is only sold online, you need something to use until you get it. Get a cheap OTO (yellow drops) / phenol test kit, or if available at YOUR Walmart (check availability), get the HTH 6-way DROPS test kit, which is compatible with the Taylor K2006. Test the pool as soon and you can, and post the results. If you get the 6-way kit, ALSO test the water you FILL the pool with, especially if it's a well, and post THOSE results as well. (The HTH is the best available kit you're likely to find locally, but it's not the K-2006. It can only provide rough measurements chlorine levels above 5 ppm, and it measures "TOTAL" hardness, rather than "CALCIUM" hardness, which is not ideal.)
We need some more info to be able to give you good advice. Can you please take a minute and fill in our pool chart?
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