Used black&white bleaching cream 3 nights in a row on cheek for dark spots. Turned face red and dry. What happened? How to fix?

Another option you can consider is IPL therapy. This is a light based therapy that can be very effective. That can reduce brown pigments, red pigments and reduce active acne. It may be useful to look into this. I recently wrote a large editorial discussing many aspects of this treatment....

Although we know hydroquinone can be a safe and effective treatment for adults, its safety has not been established in infants or children. Moreover, hydroquinone is only effective for certain kinds of pigment, and will not treat all dark spots. Babies can develop dark spots on their skin for a...

Unfortunately there is no treatment that works well for this.  This is genetic and a combination of rubbing in the area and inflammation that causes pigment production.  Topical lightening creams are never usually effective alone.  In combination with light chemical peels like...