Bleach is in fact liquid chlorine. The very same stuff pool stores and pool care companies use. The only difference is the strength. So as long as your pool water test results are in order, you can swim! Desired FC levels are individual, based on the pool's CYA (Stabilizer) levels, to maintain a clean pool.
You do have one of the two recommended test kits and test your own water.....right? If not- get thee up to the link at the top of the page and start reading "Pool School"
And yes, if you put too much chlorine in a vinyl lined pool, above what is needed and above what your CYA and algae killing level (SLAM level) is, it might hurt the liner.