Hi!
I've looked at your pictures and saw the lines which appear when you smile, so-called "crow's feet". They result from the effects from the sun combined with the repeated movements of the muscles around your eyes.
Neuromodulators(e.g. Botox, Dysport or Xeomin) generally work well around the eyes. The most frequent risk would be a bruise, but even that is the exception rather than the rule. To minimize the risk of bruising, I inject more superficially in that area.
I also saw that you have a groove where your lower eyelid meets your cheek. That area frequently benefits from a small amount of dermal filler, e.g. Belotero or Restylane.
Topical retinoids (e.g. Retin-A, Renova, tretinoin et al.) also help to reduce fine lines around the eyes.