Are you saying that:
1. You have not used the pool;
2. you waited till your skin was clear;
3. you did a bleach bath (what concentration?);
4. and now have itchy red skin?

If your answer to ALL the questions above is "Yes", the next step is to
1. Wait till your skin clears,
2. Repeat the bath EXACTLY as before, but with NO added chlorine.

Just to explain -- we have to find a "no irritation immersion' starting point. Because fresh water is intrinsically somewhat irritating (eye saline is not), and because tap water sometimes contains monochloramine to which some people are sensitive, we have to rule out those out.

It's possible that your skin is dried enough by a bath, but not by a shower, to cause problems. So please duplicate conditions exactly (time, temperature, depth of tub) minus the bleach when you repeat.

Once you find a 'safe point', we can add chemicals one at a time, till we've got enough to make up a treatment system.

It would REALLY help if you had a K2006 testkit. (http://pool9.net/tk/. We'll also need measured dimension on your tub at the fill point, in order to calculate volume, so I can calculate test doses.

Regarding your pool, you need to maintain the pH between 7 and 8, and your chlorine at 10% of your CYA level (9 ppm . . . if the store test is accurate -- but it's probably not).