I've gone to a total clean up a few years ago (think in a combination skin prone to sensitivity and sunburnts...) and one of my aunts has done it too more recently (bad experience with peeling). There are a few simple things we used that may help with your case
1) Before you reintroduce some moisturizer, you may take a day or two using just a "100% pure glicerin" soap with physiologic ph (physiologic, not neutral). Glicerin is good non-abrasive cleaner, but has also moisturizing and umectant properties. Also, since physiologic ph is less abrasive than neutral ph, it may be a good idea to keep using it so that your skin can restaure its natural defenses quicker.
2) Aloe vera sap has curative and calming properties and is a very potent "oil-free natural moisturizer". You may apply its sap as a facial mask, specially on your flakey and "moustache" areas (don't use the aloe vera oil, it is not the same thing)
3) A very good and cheap moisturizer you can use before sleep while your skin is still sensitivy is good old nivea cream (that one in a dark blue small can). NIvea cream is a very underrated product if you ask me. I had some very bad sunburnts and my auntie had a bad experience with peelings and Nivea Cream was really good help in both cases (better than other more elaborate/expensive products in fact).
Best regards,