A babies cheeks can get red when the baby is teething and red flushed looking cheeks is one of the common signs that your baby is teething.
The reason a babies cheeks are red and flushed looking while the baby is teething is due to the inflammation and irritation of the babies gums while the new teeth are pushing through the gums.
A baby can also develop a rash on their face from the drool when they're teething so wipe the babies face down often while they're teething.