Undereye wrinkles that only appear with smiling
You have what we call an #infraorbital roll from a hyperdynamic periorbital muscle. In your case, the inner fibers of the sling of periorbital muscle that surrounds the eye is very strong, and can easily be relaxed with just a few units of #Botox.
Smile Lines Under the Eyes
Your photos show a wrinkle under your eyelids that could easily be softened with a small amount of Botox. There are other measures available as well like filler but this appears to be a muscle only problem which is best addressed with a treatment like Botox. It would have to be repeated every 3 to 4 months but I believe you would get a very pleasing result.
I hope that helps.
Under eye wrinkles
Based on your age, skin texture, and very few wrinkles I feel just a small amount of Botox to the muscle around your eye will make a very nice difference. This line is due to the contraction of this muscle and it will soften nicely with a bit of Botox. Yes, Botox will have to be repeated every 3-4 months but it will give you the most natural, effective result. Please consult a board certified cosmetic dermatologist or plastic surgeon for evaluation. Best wishes.
Under eye creases
Those little creases are from the obicularis oculi muscle contracting when you smile. A small amount of Botulium toxin (Botox Cosmetic or Dysport) would work nicely.
Crease under eye
I see you have a single crease under your eye when you smile. A small amount of Botox just above the crease into the orbicularic oculi muscle usually diminishes that crease nicely.
How to Get Rid of Lines Under Eyes When Smiling. Present Since Childhood.
I would accept this as a natural smile line. It is caused by the activity of the orbicularis muscle that closes your eyes. Although it could be surgically thinned it is more natural and functional to leave it alone. If superficial wrinkles appear over time, these can be treated with any number of laser devices that soften wrinkles, such as microablative carbon dioxide or erbium lasers.
A little Botox will help those under eye creases.
The bulging and crease when you smile is caused by a muscle that activates when you smile. As Dr. Stolman mentions in her post, it's called the obicularis oculi. A little Botox into this area will help relax the muscle and thus help the bulge and crease. Botox needs to be repeated every 3 - 4 months but the amount needed will be quite small so it would not be terribly expensive. IMO, Botox is the way to go for this problem. Any surgery to reduce or weaken the muscle would not be worth the risk when Botox is available.