Is it common for babies to get rash (little red spots) around their mouth because of feeding?

It could be milk rashes. Typically, milk rashes are an allergic reaction to milk formulas or a hormonal reaction to your breast milk. At other times, these rashes can also appear if milk had dried up on your baby’s face and wasn’t wiped clean. These rashes may also appear if your child’s skin is always wet with saliva or comes in contact with harsh fabrics or chemicals like perfumes or colognes. You can use clean cloth and wet with cool-boiled water to clean baby's mouth after each milk feed. The link here has other suggestion like use jasmine flower and Wondercreams to get rid the milk rashes. http://sg.theasianparent.com/milk-rash-remedies/