It's funny, but I posted a similar question almost 2 years ago and keep meaning to come back and post what I learned . . . it sounds like teething is a possible culprit, but I wanted to second that red cheeks (esp w/chapped skin or cracking skin) are a very common sign of a food allergy.
My ds's red cheeks began around 5 mos and we were told for a *year* that they were due to teething. They never went away however, and sometimes cracked and bled, so after many many months of trial and error, we determined that he was allergic to multiple foods coming from my milk. (And then he was allergy tested at 1 yr and the test confirmed all I had figured out -- he was allergic to wheat, dairy, corn, nuts, and bananas, with banana being the only food he had ever consumed himself).
So I say all of this not to hijack your thread or alarm you unnecessarily, but in case anyone comes looking bc they have a very red-cheeked babe who might be having a reaction. (If anyone ever wants to PM me about red cheeks, eczema, allergies in exclusively BF babies, etc., please do!!!)
Hope those cheeks are just due to teething and that they'll clear up very soon!