A puffed face or body means it looks swollen and inflamed.
When we get sick, especially with an allergy or a cold, our skin can puff up. This often happens on the eyes, cheeks, and lips. Sometimes this swelling can be quite dramatic - imagine having huge, red, shiny eyes because of allergies!
How common is "puffed"?
Word puffed is considered rare in modern English. It has a balanced usage among all categories: speech, fiction, newspapers and academic texts.
Definitions
verb
To emit smoke, gas, etc., in puffs.
To pant.
To advertise.
To blow as an expression of scorn.
To swell with air; to be dilated or inflated.
To breathe in a swelling, inflated, or pompous manner; hence, to assume importance.
To drive with a puff, or with puffs.
To repel with words; to blow at contemptuously.
To cause to swell or dilate; to inflate.
Example: a bladder puffed with air
To inflate with pride, flattery, self-esteem, etc.; often with up.
To praise with exaggeration; to flatter; to call public attention to by praises; to praise unduly.