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.

Actually, I do apply it to my hand, face and my hair. But I'm not wearing any make-up because I'm not a woman. If you work in an office with air cond just apply it before you go to work at home, the oil will just absorb to your skin pretty fast. Just compare it how long it will moisturize with your previous lotion/moisturizer.

If you can afford please go nearby pharmacy and look for a soapless cleanser/body face gel like Cetaphil, got many brands but a quite expensive, RM25-30 per 200-250ml.

Olive oil for cooking also can.