Yes, sometimes children might get puffy eyes, but usually it is not serious problem. They might get these bags for poor sleeping, allergies, sinus infection or sleeping flat on the back. To provide treatment, you need to find out what caused the puffiness. If it is caused by sleeping flat on the back, then add an extra pillow to avoid the fluid accumulating beneath skin around eye. If it is allergic reaction, get him out of touching with allergens right away. Get in fresh air in the room, and use the air purifier and humidifier. If he got his sinus infected and clogged, use some salt water to flush his nostrils. You can buy it over-the-counter. Kids always need more sleeping than adults. Have him go to bed early to ensure him adequate sleeping every day, which is helpful for his healthy growing up. No matter what reason caused his puffy eyes, you can still apply some cool water compress to help reduce the puffiness.
Take it easy if your child gets eye bags under eyes. It always happens for kids who cry for a long time and then get eye bags under eyes. The eye bags will disappear next morning if your child has enough sleep (about 9 to 10 hours) at night. And if this cannot help, try to put a hot towel on the eyes, which will also help your child remove it much earlier.
It is not good for your child to get eye bags under eyes. You could help him do the warm compress to make the eyes feel comfortable. You could find the clean cloth and hot water to make your child's eyes feel moisture. You could also help the child use the paste with anti-inflammation role to release the symptom.