CeraVe carries a moisturizing/hydrating cleanser in liquid and bar form that I think you will like. It feels creamy and doesn't dry out the skin like other cleansers.
I have sensitive inflammation-prone skin and must have a low-level degree on dermatology at this point LOL. I like using CreaVe products since they are a good price and have good simple ingredient lists. My dermatologist approves of these products too, which is nice. If you can spend a little extra, you can also try La Roche Posay's hydrating cleaser too. Very nice quality products.