Will getting it injected under the eyes be effective for a youthful look?

Lately, my under-eyes have been sunken in, making me feel like I've aged suddenly, and it stresses me out every time I look in the mirror. Since there is no flesh under my eyes, my face looks hollow, and I hear people say I look tired all the time. Would filling this area slightly with filler definitely make my face look more vibrant and youthful?

But I heard that because the skin under the eyes is so thin, if you get it done wrong, it can become bumpy or bulge out like a caterpillar when you smile, making it look really awkward. A lot of people advise against it, too. I just want to naturally fill in the sunken grooves without overdoing it.

I'm also curious about how long the effects last after just one injection. I hope it lasts a long time... I'm so stressed about this lately.