This is education, not advice
The information here is written for the general reader and does not replace a personal medical consultation. It cannot tell you whether the fullness under your lid is fat or fluid, whether your lid is a bulge or a hollow, or whether either option is appropriate for you.
Neither option is a default
Nothing on this site should be read as ranking an operation above an injection, or as describing one as the sensible place to start. Each answers a different finding, both carry real risks, and the choice follows from an examination rather than from a clinic's routine.
No outcome is promised
No treatment can be guaranteed. How much a lid changes, how the two sides match, how long a result holds and how the skin settles afterwards vary between individuals, and a result is judged honestly only after the area has had months to settle.
When to seek care immediately
After either option, a sudden change in vision, loss of vision, severe eye pain, an eye that cannot be closed, or bleeding that does not stop with gentle pressure needs care the same day rather than a routine follow-up appointment. So does spreading redness with fever, or a discharge from the area that is increasing.