Just use low pH shower gel like Johnson 5.5 or Dove and any anti-bacterial soap is more strong than these two and will damage your sensitive skin.

But the main problem is your skin after shower, forget any product like lotion, moisturizer because they a are mostly water-based. The solution is to use olive oil on your affected skin right after the bath, if the oil is too messy, try it at night before sleep and you will notice a huge difference in the next day. You can drink a couple of spoon of olive oil too to improve your skin, I suggest you research a bit about what olive oil can do to your skin.

All this on my experienced, because I gave up on any chemical product that not work.

Olive oil isn't the only option, there's plenty of other oils in the market.

Try visiting The Olive Tree at 1U or Pavillion.