The chemo can make you very sensitive to sun/wind, so you need a really good sunscreen.
I am using Clinique Super City Block and that has really helped.
Yes i had similar during Chemo. I cleansed / toned with a gentle product and used a ESPA Tea Tree gel in the evening. Only used concealer when necessary if going out also covered my face with thin scarf when going out walking. I had chemo Nov - Feb so biting cold then back indoors to heat really irritated my skin.
You could log on to Look Good Feel Better. I attended one of their sessions after Chemo but wish i'd done it earlier.
Good Luck with the rest of your treatment.
Take Care Gilly x