• Filler definitely doesn't address wrinkles, so don't do it for that. Only some people are good candidates – generally the kind whose hollowness can be seen from the side of the face, rather than just the appearance of hollowness from viewing the face straight on. But each face needs to be assessed individually.
• As other posters have said, if you have any kind of puffiness in the eye area, be super-cautious, as hyaluronic acid (the main ingredient in fillers) draws water to it, so any puffiness will just be increased. Poorly placed filler, or filler placed in people who are not good candidates can also end up obstructing the lymph system around the eyes, leading to a puffy appearance (these are called malar mounds).
• Only go to a super-experienced person (I'd only go to a doctor or nurse, I'd never, ever go to a beautician for this) – if they misjudge the injection they can end up blocking a blood vessel surrounding the eye, which can cause blindness.
Also ask the person who is treating you if they are set up to administer hyaluronidase (an enzyme that breaks down the filler), and if they are experienced in doing so) if such a thing were to happen – acting swiftly is key here. A good clinic will have such contingency practices in place (including an out-of-hours number for such emergencies). A poor clinic won't.
• As previous poster said, consider whether what you really need is more volume in the cheeks, to support the area under your eyes better. A good, experienced practitioner will do this – assess the your face as a whole, rather than just hone in on one area.
• Another option to consider is polynucleotides – these improve the condition of the skin, encourage collagen (the material that gives skin structure and plumpness) to build and improve the condition of the skin around the eyes generally. Again, only ever go to an experienced, medically trained practitioner for this.
• More info from Moorfields Eye Hospital of things you need to be aware of before you have tear trough fillers: https://moorfields.nhs.uk/private/about-moorfields-private/blog-articles/the-5-key-risks-of-under-eye-filler-injections#:~:text=There%20are%20five%20key%20risks,the%20product%20beneath%20the%20skin.
Definitely take your time and be properly informed before you decide! Good luck.