Drying and tight patches of skin after trying to start a routine

Hi guys, I've used to only cleanse my face at night with an innisfree cleanser around my oily T-zone without applying moisturizer afterwards, just because I couldn't find any that actually moisturisers my skin. Then I wanted to up my skincare game so I read a few blogs and started a basic routine to cleanse twice a day, a low pH cleanser in the morning, then an oil + low pH cleanser at night, both with moisturizing after cleansing. I used the Simple Refreshing Facial Gel as my low pH cleanser and then applied Vanicream Moisturizing Skin Cream as my moisturizer. However, I have been feeling these dry rough flaky patches of skin around my face like on my cheeks and also nose (which previously were fine without much routine care lol, maybe only a lil bit dry sometimes) What should I do now? Am I cleansing too often that it is drying my face? Or is the moisturizer not suitable for my skin? I'm lost. Can you provide me some advice please? Really appreciate it!!