Have you tried Avene's Tolerance Extreme products? I had to switch to them after I developed perioral dermatitis.
https://www.aveneusa.com/concerns/skin-affected-by-cancer
I started by trying this sample kit:
https://amzn.to/2MsYNzo
It's a month's worth. I use the mineral water spray followed by the cream morning and evening; I use the cleansing lotion in the evening before the cream.
You might also look at Osmia Organics -- because perioral dermatitis leads to dry, red, flaking, burning skin and pimples, it sounds a lot like what you're suffering from. The black soap especially is very soothing and non-drying:
https://osmiaorganics.com/collections/perioral-dermatitis
In fact I'm wondering if you've seen a dermatologist for a diagnosis?
https://www.aad.org/public/diseases/rashes/perioral-dermatitis
Whatever you do, don't use topical steroids on your rash -- either prescription or non-prescription. It may cause a temporary improvement but it will come back worse. My derm put me on Oracea, a very mild antibiotic, to help clear it up, and now I'm religious about sticking to the Avene or Osmia products. I also never use toothpaste with SLS, as that is a common trigger. And exfoliation is a no-no -- either manual or chemical.
Good luck -- perioral dermatitis is awful in its own right and I'm so sorry you're dealing with it on top of cancer.