Hi as per you, the baby had developed cellulitis of one arm for which he got tretament and now you are noticing blue lip and nose. most of your history is not adequqte to reach an diagnosis. blue lip and blue nose means he/she is developing cyanosis. now cyanosis is of varying type and causes also varies. wanted ask some more questions... is your child look sick? is he/she breathing normally or there is any breathlessness? is the tongue is also blue (side/ tip of tongue)? sometimes due to cold also the lip and nose becomes blue due to vasoconstriction but these sign may also represent central or mixed cyanosis and the undertlying cause may be a serious one. i dont want to frighten you but, i ll strongly advise you to check with your pediatrician as soon as possible. he/She will properly examine the baby including his/her chest and heart and tell you better.