If your 11's aren't so strong that they show when you're expressionless, then you will probably have terrific results. Deep furrows that have made grooves in the skin will not have the same smooth result (although over time the lines will fade if the skin remains immobile long enough.)
It sounds like what you want is the line easiest to address with botox! It's pretty good for the forehead (although it can be tricky if not administered correctly and result in a creepy expression or drooping.) It's modestly useful on crow's feet at the corners of the eyes, but can't do anything for what is going on under the eyes.
I got some near/just below the corners of my mouth because I have a grumpy little bunching of muscle there. It does look nice but I have to say that it feels funny and I find it awkward to chew food, now.
I'm an RN who practices in aesthetics. Your expectations to have that one area relaxed sound reasonable. You would be surprised the number of people who have very subtle treatments that don't break the bank regularly. That type of wrinkle is caused by muscle so dependent on how deep it is, a toxin like botox should reduce it. As Whitegrenache mentioned, can also be filled if it is particularly deep.
If you know someone who has it done, get a recommendation from them and go for a consultation. You wouldn't believe the range of treatments available that give that refreshed (not plastic) look.