Please recommend a treatment for under-eye wrinkles.

In the past, wrinkles around my eyes were more prominent in the dry winter but less noticeable in the summer; however, ever since I turned 10, fine lines under my eyes have become more pronounced regardless of dryness. I can see that the elasticity around my eyes has dropped significantly due to aging, and wrinkles have settled in. Even so... My dark circles are quite severe, and with the added wrinkles, my face looks haggard and older than my actual age, which is stressful. The wrinkles under the outer corners of my eyes are particularly prominent, and when I smile, they fold in both horizontal and diagonal directions, which looks really unsightly.

What procedures are available to reduce wrinkles under the eyes? A procedure that firms the skin around the eyes and smooths out wrinkles. Please give me some recommendations. I am also curious about how many sessions are needed to see results.