My one-year-old boy has lots of small bumps around his mouth. He has eczema around his eyes, so I'm wondering if it's the same thing.

It is recommended to show the lesions around your child's mouth to a pharmacist for a proper assessment. It could possibly be eczema or a condition called perlèche, especially common during cold periods. A pharmacist will be able to provide more accurate information and guidance on how to proceed.