Sun screen after blue peel
You should use sun screen regularly, every day, regardless of the weather and regardless whether you had a peel or not. Some people peel less or not at all after peels and this should be discussed with your skin care specialist so the peel strength can be customized.
You should see the peeing about 4-5 days after the procedure. It is important to use the cleanser that should have been given to you. You need to follow up with the person who did your peel for specific instructions.
A Blue Peel is essentially a TCA (Tricloracetic Acid) peel with blue dye. The day to day healing process and the speed of healing depends on the concentration of TCA used in the peel, but essentially the process takes a full week to 10 days for the initial healing. From your picture, I am guessing that a fairly light peal was applied, as there are risks of uneven pigmentation problems in darker skin people with more agressive treatment. Expect the skin to darken considerably in the first few days followed by flaking and pealing over the next 3 to 5 days. Keep your skin moisturized and ABSOLUTELY do not pick or peal off flakes of skin. Allow the peal to progress and the flakes to come off when washing.